There were 10,000 of them, waving placards, shouting slogans and marching through Rome on a sunny Saturday afternoon.

But the demonstration, unlike most of those in Italy these days, had nothing to to with terrorism or politics. It was instead a massive tenants' protest against parts of a nes fair rent bill that has made few people here happy. And it is threatening to bring the faltering Italian construction industry to a total halt.

The fair rent bill, which ended a 44-year rent freeze when it finally went into effect last October, has lowered many rents, raised some, and liberalized the conditions under which a landlord can terminate a lease.

Many of those attending the rally were tenants who were threatened with eviction and worried about finding other palces to live. But the basic problem, and one that is creating deep social tensions here, is an acute housing shortage that the new law seems likely to make worse.

At the Rome demonstration, Communist Mayor Giulio Carlo Argan said that the capital's administration was also considering drastic steps of this type. And he threatened to resign if Rome remains "a city of houses without people and of people wihout houses."

But this type of action appears unlikely to win parliamentary approval. So far, in fact, the parliemant has decided only to raise property taxes -- by from 20 to 80 percent -- for landlords who keep an apartment unrented for more than six months.

Those landlords who do agree to rent, furthermore, appear willing to do so only if they can cheat, with the net result that a black market has quickly sprung up alongside the less profitable legal one.

In the last few months several landlords in Rome, Genoa, Florence and elsewhere have been arrested for extorsion. The principal method is to provide a "fair rent" lease but to demand an initial under-the-table lump sum or additional monthly payments in cash that, over the four-year lease period, double the rent at least.

Another "trick" is to take advantage of a loophole in the law that excludes office space from the "fair rent" rates. Nowadays most of the dwindling newspaper rental adds (down to a few columns from the pages and pages of only six or seven years ago) are for "office use only," even though the apartments are still rented to families in need of a place of residence.

On paper, the current housing situation appears less drastic than one would think, since the severe postwar shortage (37 million rooms for 47 million inhabitants) has been officially redressed. (There are now 67 million rooms for only 57 million Italians.)

But at least 15 percent of these rooms, many of which are in second homes, vacation houses, or unrented apartments, are empty. And today there is simply no place to go for youngsters setting out on their own, young married couples, or people with growing families in search of more spacious quarters.

Almost everyone these days is looking for an apartment or has a friend or relative in that situation. One woman who left her husband three years ago is still living with her two children in her mother's two-room apartment. Another freelance script writer has spent the last three years moving from friend to friend because she can't find a place of her own.

The situation has set home-seekers' nerves on edge and frequently, tempers flare. But the landlord is as much a victim of the new law as the prospective tenant.

The fair rent law, long-presented as an important reform, sets $300 as the basic cost of a square meter in the center and north of Italy and $270 for the Italian south. But to arrive at the fair rent, that figure is multiplied not only by the apartment's dimensions, but by a series of coefficients for the type of housing, the size of the city in which it is located, the area of the city in which you live, the floor you live on and the building's age and condition.

These latter clauses mean that while rents have gone up for newer buildings, they have often declined excessively in older buildings in extremely desirable "historic center" neighborhoods, with only minimal consideration made for the tenant's income.

As a result, the landlord who purchased severl apartments as part of a traditional Italian method of investing or or insuring for one's old age is now out of luck. Statistics show, in fact, that 60 percent of Italian real estate is owned by small landlords, who prefered by small landlords, who preferred such investments to savings banks or bonds.

Today that tend has been sharply reversed, with only 22 percent of family savings going to real estate, compared with 50 percent as recently as 1973. Not surprisingly, the, construction is also sharply on the wane. In 1968, 281,813 domiciles were constructed. Ten years later the figure has dropped by half, to 147,888. And the expectation is that unless the law is amended, the next few years will see no improvement at all.