Financially battered Chrysler Corp. announced today that its two top executives would work for $1 a year for the next two years.

Chrysler said President Lee A. Iacocca and Chairman John J. Riccardo voluntarily reduced their $360,000-a-year salaries to conserve cash at the troubled company and to demonstrate their commitment to the Number 3 auto company's survival.

Presumable the action also was taken to generate some good will in Congress and the administration.

Chrysler has asked the government for federal aid and the Carter administration has said that it would consider recommending loan guarantees if the company shows that it is taking steps to help itself and if it can demonstrate that it can again be profitable.

The company has lost $360 million so far this year and lost $204 million last year.

Chrysler said the Iacocca-Riccardo pay cuts are the precursor of a general corporate salary reduction program, although one likely to be less severe than that adopted by the top officers.

A spokesman for the company said the white collar salary reductions would be announced soon.

Chrysler also has put nearly 26,000 of its 110,000 blue collar work force on indefinite layoff and has said it will make selective cuts among its white collar workers.

Although there is a history of corporate executives taking $1-a-year posts in government, financial observers were hard-pressed to come up with a corporate executive who had taken a $1-a-year job for a private company.

Pay cuts of a less draconian nature, however, are common when companies fall on hard times. Iacocca and Riccardo are both millionaires and Iacocca was paid $1.5 million by Chrysler when he left Ford Motor Co. last year.

The payment was designed to replace Ford benefits he lost when he went to work for a competing company.

Chrysler has had its ups and downs in profitability over the past decade and over the past several years has been dismantling its overseas operations and selling off some of its domestic subsidaries as well in order to generate cash it needs to restyle its product line and meet government mileage requirements.

Iacocca and Riccardo contend that much of Chrysler's current difficulties can be traced to the high costs of meeting the mileage standard. Because Chrysler sells far fewer cars than its main competitors -- general Motors Co. and Ford Motor Co. -- it can spread the costs of developing new, more efficient automobiles over fewer vehicles.

Chrysler was also hit hard by the spring and early summer gas shortages and had a huge inventory of larger cars and trucks it could not sell while at the same time could not produce enough of its popular smaller cars -- the Omni and the Horizon -- because it did not have enough engines to put in them.

In order to reduce its huge inventory of unsold cars, the company -- which had sales of $13.6 billion last year -- announced a $400-a-car rebate program to all Chrysler buyers, and also reduced the cost to the dealers of many of its bigger cars.

A company spokesman said Chrysler's unsold cars and trucks numbered 36,492 at the end of today, compared with about 80,000 on August 1. Those 80,000 cars and trucks were worth about $700 million and it cost Chrysler about $2 million a week to finance them, analysts estimated at the time.

Although Chrysler's profit on most of these cars has been sharply reduced by the discount programs, its financing costs are shrinking daily and its cash flow is rising.

The company also has decided to sell its profitable realty subsidiary to come up with more cash. And its financing subsidiary -- Chrysler Financial Corp. -- has sold many of its loans to other companies, including General Motors Acceptance Corp. and Household Finance Corp.

Although Chrysler Financial is considered to be the best run of the three auto company finance companies, it was having trouble selling its paper in the market because of the problems of the parent company. Chrysler Financial makes loans to new car buyers and also makes loans to dealers in their wholesale dealing with Chrysler.