General Motors Corp. reported yesterday a $978 million second-quarter net profit, down 16 percent from a year ago despite record sales and revenue by the nation's No. 1 auto maker.

No. 3 Chrysler Corp., meanwhile, reported a $488 million net profit, down 18 percent. Both companies cited the costs of retooling factories for new vehicles and the expensive sales incentive campaigns that kept auto sales afloat during the spring selling season.

Ford Motor Co., the No. 2 car maker, has scheduled its quarterly earnings release for today. The other major U.S.-based auto maker, American Motors Corp., last week reported a $52 million net loss for the quarter.

GM's earnings per share were $2.81 compared with a net profit of nearly $1.2 billion ($3.58 a share) a year ago.

Revenue totaled $27.6 billion, compared with $25 billion a year ago.

GM said the loss was recovered partially through more business at the General Motors Acceptance Corp. finance subsidiary and improvements in productivity and pension costs.

GM's first-half results were a net profit of $2 billion ($5.92), compared with more than $2.2 billion ($6.90) a year earlier. First-half revenue was $54 billion, compared with $49 billion.

Chrysler's net earnings were $3.29 per share, compared with $596 million ($3.35) a year earlier.

However, the new figures were bolstered by a one-time gain of $144 million on the sale of Chrysler's interest in the French auto maker Peugeot.

Chrysler's revenue for the quarter was $5.7 billion, compared with $5.9 billion a year earlier. Exxon Corp., the nation's second-largest corporation after GM, said its second-quarter profits from continuing operations fell 6 percent to $1.14 billion, from $1.27 billion last year.

Exxon said its sales in the second quarter dropped 22 percent to $17.98 billion, from $23 billion.

The oil giant attributed the decline to lower crude oil prices that were cushioned by a slower decline in petroleum product and chemical prices. World oil prices have fallen to about $11 a barrel from $30 in November 1985.

Exxon said lower crude oil prices reduced exploration and production earnings, especially in the United States, noting the impact was blunted abroad by the declining value of the U.S. dollar.

Included in last year's net profits for the second quarter was a $545 million provision reflecting a court ruling that Exxon had overcharged its customers for oil pumped from the Hawkins Field near Tyler, Tex., during the 1970s. Earlier this year, the Supreme Court declined an appeal by Exxon. The judgment requires Exxon to refund $2 billion. Xerox Corp.'s net income tumbled 44 percent in the second quarter, the company said, but added that its income from continuing operations grew 13 percent because of sharply higher profits from financial services.

The strong results from financial services, led by Crum and Forster, the company's property and casualty insurance subsidiary, offset weakness in office equipment caused by weak capital spending, said David Kearns, Xerox's chairman and chief executive.

Kearns said the results reinforced the copier maker's strategy of diversifying into financial services, a tactic that was criticized by some analysts when losses at Crum and Forster were dragging down the company's profits.

Net income in the second quarter was $122 million ($1.13), compared with $220 million ($2.17) a year earlier, Xerox said.

However, those results were distorted by a one-time charge of $12 million in the 1986 quarter related to the pending sale of Century Data Systems, and $100 million in income from discontinued operations in the 1985 quarter, including a $95 million one-time gain that included profits from the sale of three publishing companies.

The 1986 quarter also included a $15 million one-time gain from a tax settlement.

Xerox said income from continuing operations grew to $135 million ($1.27) from $120 million ($1.12) in the same period of 1985.

Financial services contributed $62 million to net income in the second quarter, a 229 percent increase from $19 million a year earlier, Xerox said. Wang Laboratories reported fourth-quarter earnings of $800,000 (1 cent), compared with a net loss of $109 million in 1984.

Revenue for the quarter ended June 30 was $716.8 million, up 13 percent from $635.2 million during the same period a year ago.

For the full year, the company reported arnings of $51 million on revenues of $2.64 billion, compared with 1984 ncome of $15.5 million on revenues of $2.35 billion.

The compay reported a 9 percent increase in new orders to $2.63 billion from $2.41 billion last year. Orders for the fourth quarter were $640.3 million, a 13 percent rise over the year-ago period.