A headline in yesterday's Washington Post said erroneously that a fascist had been elected mayor of Naples. The story reported correctly that a fascist had received a surprisingly high vote but a communist remained mayor.

After years of government first by the center and then by the left, profound frustration in Naples -- the city often termed "the Calcutta of Italy" -- has produced a sharp political turn to the right.

In last month's local elections there, the Italian Social Movement, the political heir to fascist dictator Benito Mussolini, won a startling 22.3 percent of the city's vote.

More so than other Italians, Neapolitians have a tradition of hero worship and extreme voter shifts. In the 1950s and 1960s, the man on the white horse was shipping magnate Achille Lauro, a monarchist. Later, the city's major political leader was Christian Democrat Antonio Gava. In 1975 the Neapolitians' hopes for change led to a massive vote for the comunists and Major Maurizio Valenzi.

This year a large number of Neapolitans expressed dissatisfaction with both the Christian Democrats and the communists by turning to the neofascists, who nationally poll less than 6 percent of the vote.

An active and highly personal campaign in the bay city led to a victory for the party leader Giorgio Almirante. The locally ruling communists sought to counter the neofascists' appeal with posters showing the late Neapolitan comedian, Toto, winking over a caption reading "Almirante for mayor. Have we all gone crazy?" The elections left the comunists in the number one spot. But Almirante polled the highest number -- 118,000 -- of preferential votes. In this parliamentary system, voters first choose a party and then a particular candidate.

The neofascists' campaign played up the fact that after five years of communist rule, Naples still has 150,000 unemployed, several thousand homeless, a "non-Western" infant mortality rate of 27 for every 1,000 births, inadequate sanitation and social services, severe traffic problems, and overcrowding that gives each resident only 40 square inches of parkland.

Traditionally, Naples and the Italian south have been something of a neofascist stronghold, and the party played a leading role in the 1970 and 1971 riots in Reggio Calabria and the so-called Naples bread strike of 1973.

But according to Almirante, the party's Naples voters included non-neofascists weary of Italy's other political groups and eager to give someone else a chance. In a recent interview, he made it clear that the party hopes the Naples syndrome will spread to Italy as a whole.

In 1972, widespread political disillusionment, concern over a fading economic boom and explosive social problems in the Italian south combined to give the party almost 9 percent of the national vote. In last year's general elections, it won 5.9 percent, winning 31 seats in the Chamber of Deputies and 13 in the Italian senate.

The two million Italians who voted for the neofascists in June 1979 appear to include members of families with direct connections to the Mussolini regime as well as people who believe the party is not corrupt and is sincerely dedicated to a "third way" between communism and Christian democracy.

According to Almirante, 66, a controversial figure who makes no bones about his fascist past, the party's long-term goal is a "new republic that would "reflect and synthesize the values of state, society and nation." The neofascists' Italy would be one with a directly elected president responsible for choosing an executive responsible to a parliament organized along trade or corporate lines.

He downplays the fact that many party members use the straight-arm Roman salute adopted by Mussolini -- "it's hygienic, efficient and rapid," he jokes -- and says that he is against violence, which he termed counterproductive and "stupid." But despite Almirante's attempt to give the party an aura of respectability, the party has been repeatedly accused of having an ambiguous attitude toward violence.

Italy's fourth largest party after the Christian Democrats, the communists and the socialists, the movimento -- never has had governmental responsibilities, and the one attempts in 1960 to enlist its backing for a Christian Democratic government led to riots in Genoa, Reggio Emilia, Rome and elsewhere. Most of Italy's political parties seek to avoid situations in which neofascist votes becomes essential for a law's passage in parliament. The U.S. Embassy has fewer contacts with the neofascist than with almost any other Italian party.

The neofascists in Naples claim they have become "the arbiters of the situation." But neither the reconfirmation of the city's present minority four-party coalition headed by the communists or a broader coalition under a noncommunist mayor appear to be the role for the inheritors of Mussolini's mantle.

But in this sense, the neofascists may have been lucky. Recently a top Neapolitan communist described governing that city as "the toils of Sisyphus," the ancient Greek king condemned in hell to forever roll uphill a giant stone that always rolled down again.

Other communist leaders have frequently referred to their control of Naples as "a poisoned gift." Asked if anyone could successfully govern Naples, a newsdealer there recently replied in the negative. The only possibility of improvement, he said, would be "to turn the city upside down, shake out the Neapolitans, and totally repopulate the city."