Don't sell your real-estate investment and get hit with heavy capital gains taxes on your profits. Exchange your property for someone else's -- perhaps thousands of miles from where you live -- and you can postpone indefinitley paying even a cent to Uncle Sam.

That's the unofficial motto of the fastest-growing, least-publicized movement in the U.S. real estate: the professional "exchangors" or property-swap counselors."

An estimated 20,00 to 25,000 "exchangors" are active today across the country, according to leaders of the movement, a 300 percent increase during the past three years. They are most heavily concentrated in the Sun Belt and Western states, but are expanding rapidly in Northern and Eastern states.

What they specialize in is putting together tax-free transfers of real estate of almost any size, shape or location.

Let's say, for example, that you've owned a small home or duplex in your community that you've rented out for the past five years. Thanks to inflation, the value of the house may well have doubled. If you sold it at a large profit this summer, you'd have to share a chunk of your profits -- thousands of dollars' worth -- with the Treasury Department in the form of federal capital gains taxes.

Let's say, though, that you traded your house for some other type of real estate, such as a resort condominium, a small piece of farm property or an investment share in local shopping center.

With a little help, you should be able to avoid capital gains taxation completely on the transaction. As long as the equity value of your rental house -- including all you inflationary profits -- was equivalent to the value of the other owner's equity, you'd get off tax free.

In effect, you'd receive virtually all the benefits of a highly profitable sale but none of the tax liabilities.

"What you get is an interest-free loan from the federal government (on your untaxed profits) for as long as you want one -- and that's nothing to turn up your nose at," says Michael P. Sampson, professor of tax law at the University of Baltimore and an active proponent of exchanging.

The key to tax-free exchanging -- and the mushrooming growth of real estate exchange organizations -- is a once-obscure section of the Internal Revenue Code known as "1031."

Under its provisions, anyone who owns property for investrment or business purposes can trade it for property for "like kind" and equivalent value without paying a cent. Only when your truly sell your property for cash do you trigger federal taxation.

Although "1031" has been in the tax code for five-decades, exchanging as a tax-cutting technique has caught on in the real estate field only recently.

"Inflation has turned exchanging into the hottest game in town" in some parts of the United States, in the words of a tax-policy official of the Treasury Department, "and it's beginning to cost us a hell of a lot of revenue."

The official, who declined to be identified, said the federal government isn't sure how much money it's not collecting anually because of real estate exchanging, but suggested that the budget-conscious Reagan administration ought to take a much closer look.

There are no immediate plans at the Treasury or in Congress to change the law, however, the official said. That means a green light for real estate owners for at least the next two years. It also means a continued boom for property-swap groups like Interex, the Internal Exchange Association, based in Leucadia, Calif. Interex holds periodic, mammouth exchange meetings around the country, where hundreds of brokers, attorneys and property owners get together for three or four days to swap real estate.

Interex's April exchange meeting in Las Vegas produced in excess of $2 billion worth of real-estate swaps -- ranging in size from $3,000 "timeshare" interests in Florida condominium to multi-million-dollar office buildings in major cities.

"The exchange field is the wave of the future in real-estate," says Interex's ebullient vice president, Trader Drew of St. Petersburg, Fla.

"There's absolutley no reason whatsoever why anybody should pay capital-gains [taxes] to Washington today if he's seriously interested in building wealth. There are so many legitimate way under Section 1031 to exchange property -- and get everything you wanted out of the transaction -- that selling property has come to be kind of old-fashioned, out of date."

Drew noted that Section 1031 exchanges not only can save real-estate owners from capital-gains taxes, but can also achieve other tax-related benefits. Chief among these are increased depreciation deductions. An owner of a duplex or apartment building that's depreciated over five or six years can exchange into a new property, with a much higher tax "basis" or value, and start getting much higher depreciation deductions to shelter his ordinary income than were possible under the former property.

By the way, one note of caution: Drew warns that exchanging is not for everyone and carries the risk of a federal tax audit if improperly done.

(For more information on exchanging, Interex's address is Box 2446, Leucadia, Calif. 92024.)