The Italian mafia has a lot in common with Hydra, the many-headed water monster of Greek mythology. If one of Hydra's heads was severed, two new ones grew in its place. Nonetheless, Hydra was not indestructible: if fire was applied to the wound immediately, new heads did not grow. Hercules and his assistant Iolaus caught on to this, the former hacking heads, the latter applying a burning iron to the cuts. Exit Hydra.

There are modern-day Italian heroes comparable to Hercules and Iolaus. Sicilian-born judges Giovanni Falcone and Paolo Borsellino both applied intense heat to the Mafia. But living in the real world rather than the legendary, both men were defeated by the monster. Four years ago last week, Falcone was blown up by a Mafia bomb; two months later his successor Borsellino met the same fate.

But the heat goes on. The two brave judges have become martyrs for many Italians and, as indicated by last week's arrest of Giovanni Brusca on charges that include the murder of Judge Falcone, their death has helped galvanize the country into thinking the Mafia, like Hydra, has some serious weaknesses.

The criminal organization's motivating forces of greed and fear remain far stronger than those of law and order. The Mafia continues to be a vast multinational dealing in extortion, drugs, arms, real estate and money laundering. Until recently, the biggest risk run by mafiosi was internecine warfare sparked by territorial jealousies.

So what has changed, apart from the strains imposed by a few gutsy judges and a growing number of incorruptible police? The answers are political, social and economic. The fall of communism, the collapse of Italy's long-running Christian Dem ocrat Party and the decision of the Roman Catholic Church to come out of its closet on organized crime have all hurt the Mafia. On the business side, capos, like capitalists, are finding that trade is tougher than ever. The Italian Mafia and its U.S. offshoots have some increasingly powerful imitators--in Russia, Colombia and a host of other countries--capable of turning former crime monopolies into at best joint ventures. And the competition for business, for example from rival organizations such as Asian triads, is increasingly fierce.

Southern Italy offered perfect soil for the Mafia to grow. In his book Making Democracy Work: Civic Traditions in Modern Italy, American academic Robert Putnam argues that a history of totalitarian rule is often followed, as Italy's south shows, by "amoral familism, clientilism, lawlessness, ineffective government and economic stagnation." Writing in 1993, Putnam ventured that postcommunist Russia, with a totalitarian record under Czars and commissars, might be heading down the same road. "Palermo may represent the future of Moscow," wrote Putnam.

The economic stagnation of Italy's south fosters the conditions in which the Mafia thrives. Southern unemployment is 35% in parts and more than 50% among young people in some areas. No wonder Romano Prodi, who heads the governing center-left Olive Tree coalition, said the day after taking office as Prime Minister this month, "The Mafia is not the daughter of underdevelopment but the mother."

But if totalitarian traditions and the vicious circle of stagnation have favored the Mafia, modern Italian politics have positively allowed it to flourish. While the American Mafia operates as an ugly growth on that society, the Italian version is deep within the bloodstream. An example of just how intimate Italian politics and crime have been is provided by Alexander Stille in his widely praised 1995 book Excellent Cadavers: The Mafia and the Death of the First Italian Republic. While working on the book, Stille asked a Sicilian friend why he was so wary of a certain local politician, given the man's record as a public critic of the Mafia. The friend replied, "He's alive, isn't he? If he had really done anything against the Mafia, he would already be dead."

Stille, like most other Mafia authorities, points to the landing of Allied troops in Sicily in 1943 as an important step in the politics-crime courtship that has seen the Italian Mafia grow into today's three-headed body: the Sicilian Cosa Nostra of about 180 families with some 5,000 members, the Neapolitan Camorra with an estimated 7,000 mafiosi and the Calabrian 'Ndrangheta with roughly 5,000.

The Allies came along at just the right moment for the Mafia, which had been getting a hard time from Fascist leader Benito Mussolini, never a man to share power. In 1943, the U.S. War Department, the story goes, wanting as easy a landing on Sicily as possible, enlisted the aid of American-Sicilian mafiosi. The U.S. troops were welcomed to Sicily by local don Calogero Vizzini, who was made an honorary colonel on the spot and who in return presented the Americans with a list of local mafiosi who were to be made mayors of various towns.

How much of that wartime account is true is hard to discover because the U.S. State Department prefers it to stay that way. Author Stille and others have had little success in getting the records declassified. What is sure is that the Mafia quickly learned that doing favors can be extremely profitable.

Postwar, the conservative Christian Democratic Party, which thrived on fear of around-the-corner communism, reached a tacit agreement with the dons who had proved useful in wartime: the Mafia would deliver southern votes to the Christian Democrats; the organization could go about its business. In the '70s, this symbiosis that saw mafiosi as a counterbalance to communists remained real enough for veteran Italian conservative newspaper editor Indro Montanelli to advise readers, "Hold your nose and vote Christian Democratic."

How high within Christian Democratic politics the Mafia reached is still being determined, as two current trials of seven-time Prime Minister Giulio Andreotti show. Andreotti, 77, is accused of supporting the Sicilian Mafia, helping fix court cases and ordering, or consenting to, the successful Mob hit on a muckraking journalist.

Andreotti sees the case as a conspiracy against him. Part of the evidence is his association since 1968 with Sicilian politician and Mafia friend Salvatore Lima. Another accusation, by Mafia turncoat Baldassare Di Maggio, is that in 1987, he was present when Andreotti met Mafia boss Salvatore ("Toto") Riina, a predecessor of Brusca's now also behind bars. Andreotti and Riina allegedly exchanged the Cosa Nostra's ritual kiss of respect. Journalist Montanelli, 86, doubts the claim, saying Andreotti "doesn't even kiss his own children." But if Andreotti is innocent, there are hundreds of former Italian politicians who have been linked to the Mafia.

It is people like Di Maggio who have done more harm to the Mafia than any anticrime measure. Mafia pentiti, or turncoats, have been so willing to sing against former colleagues in return for immunity or leniency that today they form a queue of more than 1,000 witnesses.

Being a Mafia superinformer remains superdangerous: since the most famous of the pentiti, Tommaso Buscetta, turned state's evidence in the early '80s, Mafia hit men have killed his wife, his three sons, in-laws, aunts and uncles. One estimate is that there have been as many as 33 Buscetta corpses since his evidence began to bring down former colleagues in the famous Mafia "maxi-trial."

Apart from its legal troubles, the Italian Mafia has suffered some severe psychological blows. In recent years the church, long conspicuous by its silence, has begun to condemn the Mob. Various priests and bishops have risked their life to speak out, especially since Pope John Paul II's anti-Mafia speech in May 1993 in Agrigento, Sicily.

An increasing number of public officials have run even greater risks. For example, in the Cosa Nostra homeland town of Corleone (pop. 12,000), Mayor Giuseppe Cipriani has been outspoken against the Mafia since his election in 1994. He has even risked approaching the wives of Mafia bosses to try to persuade them not to let their sons follow in their fathers' violent footsteps. Last week, after the capture of Brusca, Cipriani took to the streets of Corleone with other residents, including 700 students, to applaud the arrest.

Another gutsy Sicilian mayor, Catania's Enzo Bianco, speaking at an anti-Mafia conference in Palermo just two days before Brusca's arrest, warned that every victory is only momentary. Said Bianco: "For every mafioso arrested there are another 10 desperate men ready to take his place." Catania, in eastern Sicily, has 40% unemployment and six Mafia trials in progress; thou sands are suspected of being Mafia members. American expert Stille was also cautious last week, but optimistic about the symbolic importance of Brusca's capture: "For 40 years the Mafia in Sicily got away with murder, literally. And people who went to prison didn't stay there very long. The arrest of Brusca shows that impunity is no longer possible." Stille would not speculate about the new head that will rise to take the place of Brusca. "What is important," argues Stille, "is that no matter who comes in, they know they are going to be under constant scrutiny and pressure, which takes away from their power enormously."

Some of that power is being transferred offshore. At a London conference of law enforcement officials last week, it was agreed that much Italian Mafia money is finding its way into ventures in Eastern Europe, especially Russia. Author Putnam, it seems, was right about Moscow's becoming the new Palermo. Major General Giovanni Verdicchio, of the Italian financial police, told the conference there were signs the Russian mafiya was using the Italian organizations to grow stronger, just as the U.S. Mafia did earlier this century. Conversely, said Verdicchio, "the Italian Mafia is laundering money out of the former Soviet Union to rebuild itself financially because of the clampdown on its domestic operations."

John Guido of America's Federal Bureau of Investigation had a chilling warning at last week's meeting: "We know a lot less about the East European criminals than we do about the Italians. We have no history of these people. Who are they? Who are their connections?"

As long as unemployment and economic stagnation remain endemic in many parts of Europe, the problem is certain to grow. But at least in Italy there are signs with the capture of bosses such as Brusca that the law is getting smarter, that at last there is the political and public will to tackle the Mafia. Nowhere is there better proof of this than in the main square of Corleone, in the Cosa Nostra heartland. In 1994 it was renamed after two modern Italian heroes: Falcone and Borsellino. The real breakthrough will come when the plaque honoring them is no longer vandalized, as it was in November 1994 by children of the mafioso Riina. Then the judges might be able to rest in peace.

--Reported by Greg Burke and Toula Vlahou/Rome and Elaine Rivera/New York