The West's automobile crisis finally has caught up with Italy, where falling demand and structural problems have combined to convince leading car manufacturers here to lay off thousands of workers temporarily.

The extent of the current difficulties was dramatized earlier this month when the state-owned car manufacturer, Alfa Romeo, declared itself to be in "a state of crisis" and announced plans to lay off or place on short time the equivalent of one-third of its 45,000-person work force.

At the same time, the giant private auto manufacturer, Fiat, said that 60,000 workers would be put on short time for two weeks in January and February. In earlier recent attempts to trim excess labor and increase productivity, the Turin-based plant put some 70,000 of its 130,000 workers on temporary short time to avoid building up excessive automobile stocks.

With losses reportedly running at about $85 million a year, Alfa Romeo President Ettore Massacesi has made it clear that failure to cut output in 1982 could jeopardize hopes for recovery in 1983, a recovery tied for the most part to plans to capitalize on new economies of scale through agreements in the components sector with Fiat and though a controversial joint venture between Alfa and Nissan of Japan.

Massacesi said earlier this month that the company, whose share of the Italian market has declined from 7 percent in 1980 to the current 6.6 percent--wanted to shut its principal factory in Varese outside Milan for 74 days in 1982 and its southern plant at Pomigliano d'Arco for 95 days.

He said 7,900 workers would be put on temporary short time, while another 6,600 blue and white-collar employes would be on a "zero-hour" layoff for the whole of the coming year. The company wants to reduce its 1982 output to 180,000 units from this year's expected production of about 200,000--about 15 percent of Italy's total automobile output--and 1980's output of 220,000 cars.

Italy's metalworkers union reacted angrily to the plan and scheduled a series of protest strikes. The unions believe that Alfa, which recently established a "production group" system to maximize productivity when high absenteeism threatens the efficiency of the assembly line, may be seeking to reduce its labor force permanently.

Fiat did this in 1980 when it rode out a lengthy and bitter strike to win the right to trim 23,000 jobs. Since then, productivity at Italy's largest private company has increased by about 20 percent. And despite the general European downturn, it has managed to increase its market shares in West Germany, France and Great Britain.

Analysts here agree that Fiat is now far healthier than its smaller rival. But both companies are expected to suffer from the general European decline that already has hurt automobile sales elsewhere in Europe.

In the first 10 months of this year, car sales here grew by about 2 percent compared with 1980. The 10-month growth rate was half the growth rate in the first half of this year and one-fifth of that registered in 1980.

The vitality of the Italian market until recently is explained largely by the inflationary spending that has become almost habitual here. More worrisome is the thriving business in imported cars.

For example, sales of imported autos here grew by 11 percentage points in the first half of the year to almost 41 percent of the total. And although Fiat is still number one on the home market (Renault is now second with 10 percent of the market and Alfa Romeo is third), its share of the Italian market--considering Fiat, Autobianchi and Lancia together--gradually has declined to 51 1/2 percent.

Fiat spokesmen like to point out that no other European car manufacturer controls so great a share of its home market. But 15 years ago that share was 75 percent, and 10 years ago it was 65 percent.

The decline is even more dramatic in the small-car segment, once Fiat's speciality. In 1973, Fiat controlled 87 percent of the domestic market, but by 1980 competition from Renault's R-4 and Citroen's Dyane had brought that share down to 73 percent.

The decline is even greater for medium-small cars. Over the last seven years, the Italian share of the home market in that segment has dropped from 80 percent to 60 percent, a loss of close to 100,000 cars.

One major mistake by Italy's two leading manufacturers was that each moved into the production segments in which the other specialized, resulting in a loss of economies of scale and the creation of what one Alfa official recently called "deformed cost structures that made us into competitors and trapped us in the Italian market."

Another problem has been heavy labor and other costs that the companies now are forced to deal with by sharply cutting back production and employment.