The loudspeakers in the locker room at the women's gym blared out the news that at least eight Italian political leaders had received new letters from kidnapped former premier Aldo Moro asking that the Italian government release several jailed terrorists in exchange for his life.

Of the 30-odd women in tights and leotards onlu a few appeared to be listening to the latest installment in the current Italian drama.One elderly woman stood shaking her head in dismay.

A few yards away several younger girls sat perched on the edge of the gym's swimming pool ignoring the broadcast and discussing the new bikinis theu were planning to buy. Conversations else where in the room continued undisturbed.

Seven weeks after the Red Brigades kidnaped Moro here in a bloody ambush in which his five police body-guards died, few Italians seem to be deeply affected by the influential politician's lengthy captivity nor by the propect of his possible death.

Opinion polls carried out by the Milan-based Doxa Institute show not only that a majority of the Italians questioned would oppose a government deal with the Red Brigades to get Moro back, but that more people were affected by the death of the five policemen than by the kidnap of Moro.

Most observes here believe that the attitudes of cynicism and indifference that seems to prevail here reflects the average Italian's deep seated distrust and dislike of the politicians who have run this country since World War 11.

At a downtown beauty salon one day this week, a number of young and middle-aged Roman women sharply criticized the small Italian Socialist Party for favoring a deal with kidnapers then exchanged jokes about the Moro case, most of which involved puns based on the fact the word Moro can mean "dark-haired" in Italian and "I am dying" in Roman dialect.

One foreign psychologist who visited here recently suggested that the widespread black humor may represent some kind of collective defensemechanism.

More than 30 years of inefficient government and recurrent scandals have led most Italians to believe that Italy's "political class" consists almost entirely of men who are either dishonest or unconderned about their country's welfare.

Morro, whose family has always lived in an unostentatious manner, has never been tarred with the brush of corruption. But as an administrator he failed to give his countrymen the impression that he was concerned with their day-to-day problems.

Unfortunately, Moro's letters from captivity, primarily a cry for help, have done little to erase that impression. Most Italians are aware that Moro may have written them under duress. But many of those who have read them nevertheless appear shocked, as one businessman's wife put it, "that in them there is not one word for Italy or for the Italian."

It is therefore, not suprising that many people here seem unconcerned about whether or not Moro is released alive. The latest "Moro joke" going around Rome tells, in fact, of a new communique from the Red Brigades which, says "Free 13 jailed terroists or else . . . we'll give Moro back."

And even one loyal Chritian Democrat who knew Moro well said recently that if the former party strategist were released alive, the party would not only have to get along without him but would "have to forget him as well."

During the last three decades Italians appear to have accumulated considerable rage and resentment against the privileges that many politicians have taken advantage of the enjoyed over the years.

Thus, when Enrico Savino, 31, a waiter in a central cafe heard last month that Pope Paul had made an unusual first-person appeal to the Red Brigades for the life of his friend, Aldo Moro, he was enraged.

"Why didn't the Pope go down on his knees for Christina Mazotti?" he snapped. Savina was referring to a 16-year-old kidnap wictim whose body was found in 1975 in a garbage dump and whose case - judging from its frequent mention - appears to have brought home to Italians the violence in their society much more than the attack on Moro.

Italy has always been known for its general "life must continue" attitude, but several recent visitors who know this country well have been struck by the attitude of unconcern prevailing among average Italian at a time when the newspaper headlines are even gloomier than usual.

Late last month one American tourist was surprised when a depressed looking waiter admitted to being in poor spirits "not because of Moro, but because it has been raining for three weeks."

Another told of riding past the headquarters of the Christian Democratic party and hearing the cab driver say he wished "the Moro business" would be over "because the traffic has gotten impossible.