In the second quarter, it appeared that corporate America's ship had finally come in.

Extraordinarily large second-quarter profits buoyed corporate executives who had been waiting three years for the administration's promised rising tide of anti-inflation policies to lift their boats. News of improvements in profits for companies supplying appliances, cars, air travel, banking services and oil products has helped the stock market sail on near-record trading.

However, it is a bit too early to claim complete success. While some companies see smooth sailing, others--even in the same industry--are traveling troubled waters. Moreover, when the recent bountiful increases in profits are examined in real terms, improvement is modest, although some improvement is better than none at all.

And although companies report that their cash-flow positions have improved markedly since last year, some economists said half of that new liquidity is going toward paying off old debts rather than toward investing in new plant. For example, the formerly near-bankrupt Chrysler Corp., now swimming in $1.5 billion in cash and securities, recently said it would repay early $800 million in federally backed loans after paying off $400 million last month. Both actions together saved Chrysler $56 million a year in interest charges.

Since investment is down, companies such as steelmakers and machine-tool producers that traditionally have supplied goods to the consumer industries are not faring as well and must wait until the recovery is further along. Although government tax breaks have helped business, high interest rates may be holding them back.

"There's a tendency toward euphoria with these earnings reports," said Jerry Jasinowski, chief economist for the National Association of Manufacturers. But he warned against placing too much emphasis on wildly high profit reports during the second quarter "because it doesn't address severe problems we're moving out of."

Jasinowski said that after adjusting for inflation and taxes, profits in the fourth quarter last year were slightly worse than profits in the fourth quarter of 1965, a relatively prosperous time nearly 20 years ago. Real corporate profits have fallen by more than 30 percent since 1978, he said.

"Second-quarter profits are nothing to crow about when adjusted for taxes and inflation in view of the long-term liquidity problems of industry and the low base from which the profit gains are being estimated," Jasinowski said. "We're going to see some extraordinarily large increases in profits in the second half because sales will be up due to the recovery, costs of raw materials and labor are down and firms have slashed their break-even points across the board."

Business' future problems can be traced to their entry into the recession "in relatively poor financial condition," said Robert Ortner, Commerce Department chief economist. Companies must first restore liquidity and rebuild their balance sheets.

According to Data Resources Inc., after-tax profits, following a 14.8 percent decline last year, are expected to grow 11.9 percent this year, 21.7 percent next year and 16.3 percent in 1985.

The engine behind most of this push has been consumer spending, powered by increases in personal income. In 1983, personal income is expected to rise at a 6.5 percent annual average with growth forecast at 8.7 percent next year and 8.4 percent in 1985, according to DRI.

"There's been a change in consumer psychology," said David Taylor, a retailing industry analyst for Prudential Bache Securities, who attributed the change to lower inflation, news about the economic recovery and reduced interest rates. "I think consumer psychology is taking a turn for the better." Retailing industry profits last quarter were "super," Taylor said. "Companies have expenses very well under control. Interest expense is down, too."

However, some industries, like airlines, got mixed results.

"It is clear that the financial crisis for American business of the last few years has ended," economists Allen Sinai and Andrew Lin said in a report for DRI. "Business balance sheets and liquidity are on the mend, but the pace of improvement now in prospect is too slow to prevent additional failure fallout for much of this year."

Sinai and Lin, in remarks similar to those of Jasinowski and other economists, warned that not until 1984 or 1985, when liquidity and business balance sheets are again strong enough to allow firms to purchase capital, "will most of the threat to the viability of many American corporations finally be removed."

The liquidity of nonfinancial corporations relative to spending during the second quarter grew due to increased profits, tax savings from smaller capital gains on inventory profits and fewer outlays for inventories, Sinai and Lin said.

Other improvements in business balance sheets were made through gains from the Accelerated Cost Recovery System that allowed companies to depreciate machinery and plants faster than before the new depreciation schedules were made law two years ago, economists said. Morgan Stanley & Co. Inc. estimated that cash flow should increase by $14 billion this year and by $21 billion next year from accelerated cost recovery.

Tax cuts passed in 1981 and 1982 should enhance business' coffers by $16.2 billion this year, $24.6 billion next year, by $32.9 billion in 1985 and by $38.6 billion in 1986, Ortner said. However, he warned that what the government may give business it may also take away through high interest rates.

Despite gains from tax cuts, business investment is expected to rise only slowly, partly because of the low levels of capacity utilization expected for this year and the next, Morgan Stanley said.

So while two- and three-digit jumps in profits--such as the 109 percent second-quarter profit improvement for Chrysler--have provided a silver lining, the clouds still hang over the economy. Industries still facing pressure, according to Sinai and Lin, are agriculture, agricultural machinery, air transport, aluminum, copper, lead, zinc, oil drilling and steel.

For the second quarter, the steel industry "still has red numbers and smaller losses," said David Healey, an analyst with Drexel Burnham Lambert Inc. The industry has experienced better volume through increase in steel production and shipments. The low point of the industry was last year when it operated at 29 percent of capacity. That number has now risen to about 56 percent or 57 percent of capacity, Healey said. The firms will still see red during the third quarter and gradually fade to black in the fourth quarter, Healey predicted.

Auto industry profits are on the rebound. "They cut costs, closed plants, fired people," Healey said. All of the auto companies also cut white-collar employes. "The companies had a full-scale depression on their hands."

The automakers bounced back through higher sales and a greater mix of sales, particularly in the higher-priced, higher-profit models, Healey said. Because of better gas mileage in the larger cars and lower gasoline prices, people now "are buying the cars they really want instead of the cars they felt they should have," he said.

The retailing industry will continue to improve because of higher sales and cost-cutting measures such as rescheduling employes, saving on lighting, heating and air conditioning, rerouting truck routes, refurbishing existing stores instead of expanding, and improving productivity with new computer systems, Prudential's Taylor said. Business also looks brisk for the fall and winter, but percentage gains won't be as large next year as they were this year, Taylor said.

Airline industry results have been mixed. American Airlines, for example, reported second-quarter net earnings of $39.6 million, up from $466,000 a year earlier, while Eastern lost $33.7 million last quarter. Eastern blamed its loss on discount fares and the threat of a strike.

Many airlines will fare better next quarter because of improved traffic from summer vacations and modest increases in some fares, said Eliot Fried, analyst with Shearson/American Express Inc. In addition, all of the marginal carriers have gotten concessions from their unions to improve their profit pictures, Fried said.

Higher new home sales and replacement demand is helping the appliance industry toward a 40 percent increase in earnings this year, according to Thomas Czech, analyst with Blunt Ellis and Loewi Inc. The boom will last "as long as interest rates are down, personal income is up and housing is up," Czech said. Net income for one major appliance maker, Whirlpool Corp., rose from $36.21 million to $40.68 million during the second quarter, largely due to increased sales of kitchen ranges, dishwashers and laundry equipment, the company said.

Profits generally were up for oil companies because OPEC "is bringing order back to the market," said Daniel F. McKinley, analyst with Smith Barney Harris Upham & Co. During the first quarter, oil companies cut prices in an attempt to generate sales but didn't sell any more than if they hadn't cut prices, he said. However, during the second quarter, OPEC's crude oil prices declined, while the oil companies increased their prices at the pumps, thereby pushing profits up.