If Greyhound Corp. ever rewrites its advertising slogan, the new wording might well be "Go Greyhound -- and Leave the Flying to Us."

That's because the nationwide bus company, whose customers steadily are being lured away by low-priced, post-deregulation upstart airlines, is also in the aviation business.

Greyhound owns big jets that it leases to the very airlines that are competing with its buses for passengers. Greyhound is leasing three giant A300s to Pan American World Airways and has just bought -- for more than $30 million -- a dozen British Aerospace Jetstream 31 turboprop planes to lease to small commuter airlines.

The bus line is one of a sizable number of nonaviation companies that own planes it leases airlines.

The airliner owners range from Potomac Electric Power Co. -- owner of a half interest in one Boeing 747 -- to General Electric, whose fleet of 160 commercial airliners is almost as large as that operated by Trans World Airlines, the nation's fifth-largest airline. GE also owns 30 smaller jets.

Pepco, through a subsidiary called Potomac Capital Investment Corp., last year purchased a 45 percent stake in a 747 that is leased to Singapore Airlines Limited for 15 years.

Other major owners of commercial airliners include the financing subsidiaries of Chrysler Corp., General Motors Corp., Ford Motor Co., BankAmerica Corp., Xerox Corp., International Business Machines Corp., Westinghouse Electric Corp. and Merrill Lynch & Co.

These companies are helping to fill a need, because many of the airlines are strapped for cash and must lease a large portion of their fleets.

For owners of leased airliners, there are enormous tax advantages. Investment tax credits and accelerated depreciation enable the plane owners to shelter income from other sources. Many of the airlines cannot take advantage of the tax shelters because they do not have enough income to shelter.

TWA leases 42 of its 165 planes. Western Airlines owns only half of its 82 aircraft. Financially ailing Eastern Airlines, which operates 290 planes, has 88 of them on lease -- mostly large craft representing about one-half of the dollar value of its fleet.

Even prosperous United Airlines has one-quarter of its carrying capacity on lease, mostly its larger planes. "It becomes more cost efficient," said John L. Cowan, UAL's vice chairman and chief financial officer.

Richard F. Walsh, director of the office of economics of the Transportation Department, calculates that the number of planes leased by the 21 largest airlines, the so-called "majors" and "nationals," rose by 39 percent between the end of 1978, when these airlines were leasing 435 planes, and June 30, 1985, when the figure was 605. In 1978, 19.6 percent of all airplanes operated by these airlines were leased; by June of last year, the percentage had risen to 25.5 percent.

Of the roughly $34 billion worth of flight equipment being used by all airlines, 20 to 25 percent is leased, according to William M. Hawkins, a vice president of the Air Transport Association of America, the trade group of the U.S. airlines.

"Long-term leasing has become the predominant method of financing new and used aircraft," said Morten S. Beyer, president of Avmark Inc., a worldwide aviation marketing and management service. "Cash-short airlines, sky-high aircraft prices, razor-thin profit margins and hungry manufacturers are all contributing to the development of leasing as the preferred way to finance new planes."

Both the airlines and the companies that lease planes to them benefit from such arrangements.

For the leasing companies, it is a way of sheltering some or all of their income from taxes.

For the airlines, the benefit comes in not having to invest in expensive jet aircraft, while paying the usually lower cost of leasing. Furthermore, some airlines are either so new or in such poor financial condition that their poor credit makes it difficult for them to obtain any kind of financing for new equipment. They must lease their airplanes.

In a lease, the airline has no investment in the plane. And, through a lease arrangement, it cuts its monthly payments by more than half.

"There's no question it saves you money on debt service," said C. J. David Davies, vice president and treasurer of Pan Am. "But it's a little bit misleading, because you are giving up the value of the plane at the end of the contract, and you have lost the tax benefits that go with ownership."

Nevertheless, Cowan of United said the savings from leasing are great. In some cases, he said, the tax benefits that United passed on to lessors are worth between 25 and 30 percent of the cost of the plane. And he said the savings to United from leasing -- rather than buying -- a DC10 could range from $20 million to $40 million over the life of the aircraft. He said that the total savings to the airline from leasing planes has ranged between $150 million and $250 million a year.

Such business is profitable for the lessors, too. They do not like to talk about it, but observers say that their return on investment from aircraft leasing is more than 20 percent. "We have certain corporate hurdle rates," said Robert W. Bertrand, president and chief executive officer of Greyhound Leasing & Financial. "Greyhound is looking for a minimum after-tax return on its shareholders' equity of 15 percent, and we meet or exceed that."

But such leasing arrangements are threatened. The version of the tax revision bill passed by the House eliminates the investment tax credit and limits the use of accelerated depreciation. The Senate version eliminates the investment credit but preserves accelerated depreciation.

The investment tax credit has been suspended twice -- from 1966 to 1967, and from 1969 to 1971. The ATA warned that doing away with the credit now would be a disaster for the airlines as well as for other segments of the economy, and that business investment would be decreased significantly.

One recent study showed that 83 percent of airplane buyers would not have purchased the planes had it not been for the investment tax credit.