In that economic gulf between the continents of government and business stretches an archipelago of nonprofit groups that trace a vast and varied path.

Neither altogether private nor public, they draw revenues from both sectors and in turn provide services given special value by lawmakers. As the population that supports them has grown, so has their number, only their growth has been faster and today they crowd the fund-raising waters.

Some, such as hospitals, museums, universities, libraries and symphony orchestras, stand for broad public needs and concerns. Thousands more, including industry trade associations, chambers of commerce and professional societies, serve narrower interests. There are civic groups like the Boy Scouts and religious ones like the Knights of Columbus; "public interest" lobbies like Ralph Nader's Congress Watch or the Sierra Club; and all manner of local community associations from bottle-recycling groups to PTAs.

A few are huge and occupy palaces, like the American Association for the Advancement of Science here or the Ford Foundation in New York; others get by with a part-time clerk and an unpaid secretary-treasurer. Some are run and staffed by expert professionals, others by volunteers.

Some, like the United Way and the American Cancer Society, are well-known. But have you ever heard of the American Acupuncture and Herbs Research Institute? the New Alchemy Institute? the Zen Center of Los Angeles? the Mothers Club of Stanford University? the Sons and Daughters of Idaho Pioneers? the New England Society of Little Wanderers? or the World Affairs Council of Syracuse, N.Y. ?

In all, one authoritative study claims there are 6 million such groups in the United States. No other nation has so large and vigorous a third sector. Its antecedents reach far back in the American experience. Alexis DeTocqueville wrote 144 years ago that "Americans... are forever forming associations."

Yet despite its history and importance, the nonprofit sector is one of the least charted regions of American society. It frequently goes unchallenged because its reasons for being are so basic to us: preserver of individual initiative, champion of voluntarism, sponsor of social experimentation and all that.

Its presence, though, has swelled significantly since the time of DeTocqueville's visit, and today the nonprofit sector:

Has outlays exceeding $80 billion, more than the total sales last year in the aerospace and steel industries combined.

Owns one-ninth of the land in the U.S.

Employs 5 million people, or about 6 percent of the national total, and has payrolls topping $36 billion, or nearly 5 percent of the U.S. wage bill.

Has employment that also has been growing faster than for the nation. In the charity sector alone, employment has increased an average 2.7 percent annually versus a national average of 1.7 percent.

Most of these figures come from the 1975 report of the Filer Commission, a privately initiated and privately funded citizens' panel organized by John D. Rockefeller 3d to study the nonprofit sector. The report provides the most up-to-date numbers on the dimensions of the sector and just about the only such numbers available anywhere.

The commission had recommended establishment of a permanent national agency on nonprofits. It was never done. Former Treasury Secretary William Simon did set up an advisory committee, but his predecessor, W. Michael Blumenthal, had it eliminated.

Nor has the sector received anything more than sparse and discontinuous attention from the academic community. It's not an area that traditionally trained economists feel comfortable shuffling around in. A year ago, Yale University set up a five-year program of study on nonprofits, but the project still is barely off the ground.

In a provacative exercise, Dale Hiestand, a Columbia Business School professor, recently combined figures for the nonprofit sector with those for government to show how far the U.S. economy has drifted from the private-enterprise model the textbooks still say America resembles. He found that this super not-for-profit sector now accounts for about half the jobs in the U.S.

A nonprofit organization is not barred from making a profit. What gives a nonprofit its special status is the prohibition against distributing any profits it might make to the people who control the organization.

Many nonprofits don't pay income taxes. Some are exempt from property taxes. The Postal Service also gives nonprofits a break, moving their mail at only one-third of the commercial cost. (Congress reimburses the service for the difference.)

From time to time, abuses of these privileges pop into the headlines. Boys Town, the Pallottine Fathers' Baltimore Mission and the Congress on Racial Equality are only a few of the more recent subjects involving allegations of misused funds. Fraudulent soliciting is a continuing concern of state attorneys general. And watchdog groups cite instances of self-dealing between directors of nonprofit groups and outside organizations, as well as excessive salaries being earned, lavish expenses paid, sprawling offices built and large staffs hired.

But critics and defenders of the sector alike claim that only a small minority of nonprofit groups are guilty of misdeeds or questionable practices. "There's no real trend toward abuse," said Joseph Tedesco, chief of the Internal Revenue Service division that audits nonprofits.

Sandwiched as they are between government and business, nonprofit groups are bound to rub up against the powerful interests of these other two sectors. And it is here, in the frictions which develop, that the deeper concerns about nonprofits lie.

Tax-paying businesses have complained bitterly about nonprofit associations capitalizing on tax and postal breaks to compete against them. They say some nonprofits have strained the definition of nonprofit, owning restaurants, factories and insurance firms. The Greenbelt Consumer Coop in Washington, for instance, runs a travel agency whose trips are featured in a newsletter the association mails to members at nonprofit rates.

One recurring source of tension is the magazines published by nonprofit associations. Some of the more successful ones -- National Geographic, the Smithsonian, Nation's Business and Today's Education -- go after the same blue-chip advertisers that private-sector publishers are trying to lure.

"They weren't given tax exemptions so they could go into the publishing business," said Robert Saltzman, general counsel for the American Business Press, which speaks for the publishers of specialized business magazines. "The sale of advertising and its promotion is an exploitation of their privileges."

Government officials, too -- particularly at the state and local level -- gripe about the exemptions granted nonprofit groups, looking desirously after the property taxes churches, universities and hospitals otherwise would pay. The current tax revolt fever and its resulting pinch on government budgets only aggravates the issue.

Many of the privileges granted nonprofit groups are not the result of any planned legislative scheme but have been enacted over a period of 80 years by a variety of legislators for a variety of reasons. Congress has made several incomplete attempts to address general complaints and guard against some abuses.

In 1950, it started taxing income from nonprofits' "unrelated businesses," though just what constitutes an unrelated business is still subject to legal wrangling. In 1969, it slapped a tax on advertising revenues earned by the nonprofit publications, though exceptions persist.

Congress also imposed stringent guidelines on foundations, spelling out restrictions on investment practices and setting stiff fines for instances of self-dealing. But it failed to strap the same limits on charities and other nonprofit groups. Legislators also declined to establish the public disclosure requirements for nonprofits sought by watchdog groups.

The result is that it remains difficult for the general public to obtain current information about the finances and administration of many foundations and other nonprofit associations. For instance, only 465 of 26,000 foundations publish annual reports on a regular basis, according to the National Committee for Responsive Philanthropy here.

The nonprofits are sure Congress isn't through with them. In 1974, the IRS set up a new office specifically to audit nonprofit groups, and since then, the service has reviewed all foundations and the 1,500 largest tax-exempt organizations at least once.

Greater government concern for the accountability of nonprofits is only natural given what officials note has been a significant increase in the public funding of this sector.

"It's a myth that this sector is supported mostly by the benevolence of the private sector," said Gabriel Rudney, assistant director of the Treasury's Office of Tax Analysis and former research director for the Filer Commission study. "What the figures actually show is that government contributes 34 percent of all revenues collected by nonprofits, not counting the religious groups."

Closer scrutiny from without is only one of the worries nonprofits have. Also of concern these days is the changing nature of the sector, particularly the advent of new associations -- consumer groups, environmental groups, womens' rights groups and others -- prone more to advocacy and political action than to social service in the traditional sense.

United Way, the largest charitable fund-raising association in the country, is now under attack in courts in California, St. Louis and Washington by the National Black United Fund, health agencies and others seeking a greater slice of the old pie.

Seeking to join forces for the first time and create a concerted lobbying committee, a number of nonprofits have been swept in under the political umbrella of the Coalition of National Voluntary Organizations (CONVO). But about 100 other groups -- again, mostly the newer, activist ones -- have formed a separate super association of their own, the National Committee for Responsive Philanthropy (NCRP).