Ford Motor Co. yesterday reported record third-quarter earnings of $703 million, boosting its net income for the first nine months of 1987 to $3.7 billion -- $408 million more than it earned in all of 1986.

Ford's earnings per share for the quarter amount to $2.76, compared with $2.61 a share on earnings of $693 million in last year's quarter.

The company's $3.7 billion ($14.34) profit for the first nine months of the year compares with $2.5 billion ($9.33) in net income in the same period of 1986.

But the good news at Ford is not likely to be repeated at General Motors Corp. and Chrysler Corp., both of which are expected to show significant declines in third-quarter profits, according to auto industry analysts polled by Automotive News, a trade journal based in Detroit.

GM and Chrysler plan to issue quarterly earnings statements today.

Total third-quarter earnings for the Big Three car companies will amount to nearly $1 billion, about 20 percent less than their combined income of $1.3 billion in the year-ago period, the Automotive News panel said.

GM, which has been struggling to cut costs and increase vehicle sales, will be the biggest loser with a projected 62.1 percent decline in third-quarter earnings, falling to $100 million from $264 million in the same period last year. Chrysler will have finished the quarter with $235 million in net income, a 27.4 percent drop from $324 million earned in the third quarter of 1986.

Auto industry analysts and officials pointed out that the third-quarter ended Sept. 30, before the beginning of the wildly erratic swings in the stock market, which could have a negative influence on consumer confidence.

"We've been tracking vehicle sales daily; and to be very honest about it, we see very little change in the auto retail market in response to the fluctuations in the stock market," said L. Ray Windecker, Ford's auto market analyst.

Before the stock market began its frenzied dance, auto industry experts were predicting sales of 15 million cars and trucks in the United States for 1987 -- marking the third year in a row that vehicle sales have come in at 15 million units or higher. "We see nothing, at this point, to offset that trend," Windecker said.

The projected smaller earnings at GM and Chrysler will result from a variety of factors -- including the cost of sales incentive programs used to lure buyers into showrooms, analysts said. Also, GM and Chrysler, more than Ford, have been losing market share to foreign competitors who are building and selling vehicles in the United States.

Ford's worldwide dollar sales for the third quarter totaled $15.2 billion, $881 million better than its performance in the year-ago quarter. The company sold 1,239,000 vehicles worldwide, 96,000 fewer than it sold in the third quarter of 1986.