The Buckley family of Connecticut has gained a measure of fame over the years, mostly by force of the personalities of the clan's two most public members -- the glib political commentator and writer William F. Buckley Jr. and the conservative former U.S. senator James L. Buckley, now a member of the Reagan administration.

For investors in its oil, gas and mineral interests, however, the family's most important member has been 61-year-old John W. Buckley. Until now, the businessman Buckley has assiduously avoided the kind of publicity that his brothers have courted while he quietly took care of the family's fortune.

But that may end soon. After a 3-year federal investigation, the Securities and Exchange Commission has authorized the filing by the staff of a civil suit alleging violations of federal securities laws by John Buckley, certain corporations and others.

Under John Buckley's management, the legacy of founding father William F. Buckley Sr. over the years has helped finance the family's various conservative political, literary and economic endeavors and has given its members a social status that normally comes with old wealth.

The family finances were managed through Catawba Corp., a company established in 1948 by the senior Buckley and operated out of a Manhattan brownstone.Catawba provided geological, geophysical, financial, accounting and other technical services to the six publicly owned companies that were allegedly directed by Buckley interests.

When William Sr. died in 1958, each of his eight surviving children -- and their heirs -- were left a 9.8 percent interest in Catawba. They are: John, Priscilla, William Jr., Patricia Buckley Bozell, F. Reid, trustees for Carol Buckley Charlton, Jane B. Smith and James Buckley. Trustees for the estate of two deceased daughters, Maureen Buckley O'Reilly and Aloise Buckley Heath, hold 9.8 and 7.8 percent respectively. Benjamin W. Heath, the latter's widower, has a 2 percent interest, as does C. Dean Reasoner, a Washington attorney who also is a Buckley business associate.

But Catawba was in turn financed by fees and royalties from the six companies whose stock was owned by the investing public but whose operations allegedly were directed by the Buckley interests.

Because these companies were owned by the public, their operations -- including their relationship with Catawba -- were subject to the federal securities laws. In 1978, after the SEC began its probe, Catawba ceased offering the services to the publicly owned companies.

Now, according to public records, the SEC suit alleging securities violations will name, in addition to John Buckley, his brother-in-law and business associate Heath, the lawyer Reasoner and Catawba. In public filings with the SEC, two Buckley-controlled companies said they were informed that the commission authorized a suit against them in connection with "fees and royalties paid . . . Catawba."

The six public companies, all in the oil exploration business, are Pantepec International Inc., Coastal Caribbean Oils & Minerals Ltd., United Canso Oil & Gas Co., Canada Southern Petroleum, Pancoastal Inc. and Magellan Petroleum Corp.

A central question in the SEC's case and in a private stockholder suit already filed is what Catawba did to earn the fees and royalties. The lawsuit, filed in 1977 by a United Canso stockholder and still being litigated, alleged that the services purportedly furnished by Catawba "were as well provided by United Canso's own staff, and . . . were often inadequately performed by Catawba or not performed at all."

The 1977 suit by the two stockholders accused Catawba, John Buckley and others of defrauding the public company and the shareholders of $3.1 million in royalties paid Catawba in connection with the sale of United Canso's North Sea oil rights.

A federal judge in Hartford, in denying a defense motion to get the law suit dismissed, wrote in an opinion that if the allegations in the complaint were proven, then "some or all of the defendants were involved in illegal self-dealing and disloyalty of the highest proportion."

That stockholders' suit apparently attracted the interest of the SEC, which soon after began a formal investigation.

SEC officials refused to comment about the Buckley investigation. An attorney representing the family interests also declined comment.

Last year, another group of angry shareholders mounted a palace revolt at United Canso. In July, the group -- composed of conservative oilmen from Texas and Canada -- succeeded in overcoming a protective mechanism to ward off challengers by limiting stockholders' voting rights. The persistent rebels expelled the Buckley forces from the board of the company and threw United Canso's resources behind the stockholders' suit against Catawba and the Buckley interests.

The story of the Buckely fortune dates back to the early 1900s, when the young William Sr. divided his time between practicing law in Texas and searching for oil in Mexico. When not wildcatting, Buckley pushed his form of conservative capitalism in Mexico with a zeal that he would pass on to his children.

But apparently Buckley backed the wrong Mexican general. According to the book "The Buckleys, A Family Examined" by Charles Lam Markmann, Buckley was expelled from Mexico in 1921 for "his involvement in the opera buffa failure of a counterrevolutionary movement."

Buckley had founded Pantepec Oil Co. of Mexico (now Pantepec International). Once expelled, he switched his oil exploration efforts to Venezuela.

At about this time, the senior Buckley moved his growing family to suburban New York and then to an estate in Sharon, Conn., which is still in the family. Meanwhile Buckley sought financing for his ventures on Wall Street, and his early backers included E. A. Pierce, a founder of the brokerage now known as Merrill Lynch, Pierce, Fenner & Smith Inc.

Buckley apparently proved more adept at raising money than oil, earning him the nickname "Dry-hole Bill," according to several reports of that time. But just before World War II, he made a major strike on Pantecpec land in Venezuela, and the foundation of the Buckley fortune was laid.

After the war, Buckley searched for oil in the Middle East, Greece, Latin America, the Phillipines and Australia. To finance the search, he formed a number of companies and sold stock to the public.

It there was one characteristic of all the companies, it was that the Buckley interests retained absolute control over them, even though most of the companies' stock was held by the public. Indeed, while the Buckely interests have held very little stock in the public companies that Catawba serviced, they nevertheless dominated the companies' boards of directors.

In the United Casno case, Buckely had structured the company so that the stockholder was allowed a maximum of 1,00 votes in a proxy contest no matter how many shares he might own.

Public filings show that, over the years, the relationships among the six companies themselves, and between each of them and Catawaba could be accurately described as inbred:

Pancoastal in 1979 sold a 17 percent interest it held in Pantepec to United Canso for $1.1 million. According to documents filed at the SEC, $930,000 of that money was used by Pancoastal to pay debts owed to Catawaba, John Buckley and members of the Buckley family. In October 1980, Pancoastal -- whose chief asset had been the 17 percent share of Pantepec -- declared bankruptcy.

John Buckley concurrently served as a director of Coastal Caribbean, president and director of Pantepec, chairman and president of United Casno and of Canada Southern, director of Pancoastal and chairman of Catawaba.

Heath was chairman and president of Coastal Caribbeana and of Magellan, director of Canada Southern and of United Canso and president of Catawaba.

Reasoner was a director of Magellan, Coastal Caribbean and Pancoastal. He also was the only nonfamily stockholder in Catawaba.

When Catawba ceased servicing the six companies in 1978, two employes and trusted associates of the Buckleys, Arthur B. O'Donnell and Frank P. Gherardi, founded a firm of their own, them replaced Catawaba as management consultants to the six companies.

The Buckleys' clash with the SEC had its origins in 1971 when United Casno acquired a 20 percent working interest in a license to explore for oil and gas in the North Sea. But United Casno soon had trouble meeting exploration expenses that approached $150 million. So, under threat of forfeiture, it sold its interests in 1975 to a West German company for about $57 million.

Under the terms of Catawaba's management contracts that terminated in 1978, the consulting firm collected 1/64th of any royalties earned by the six companies. The 1977 suit charged that the Buckleys who were stockholders and directors of both Catawaba and United Casno claimed that Catawaba was owned its royalty on the North Sea sale -- even though no oil had been discovered by the time it was sold.

Two United Casno directors, Albert Barton and Austin G. E. Taylor, were picked to decide what the royalty payment should be. The 1977 lawsuit charges they were chosen because they had no interest in the oil royalties. But, said the suit, Barton was a long-time business adviser to the Buckley family, and Taylor was Bill Buckley's brother-in-law.

Barton and Taylor allegedly a petroleum engineer, who claculated that the United Casno portion of the North Sea oil eventually would be worth $200 million -- if it had not been sold to the West Germans. So they figured Catawaba should collect 1/64th of $200 million, or $3.1 million.

The money was paid to Catawaba and distributed among its shareholders.

The suit by the United Casno stockholders accused John Buckley, James Buckley, Heath , Reasoner, Taylor, Barton, Austin, Catawaba and other of fraud against the company and its stockholders.

Now it's the SEC's turn, and its suit apparently can be expected any day.

This would mark the second time in as many years that a Buckley has had a run-in with the commission.In 1979, the SEC filed suit against William F. Buckely Jr. accusing him of violating the antifraud statutes for allegedly attempting to avoid personal bankruptcy by selling some of his losing personal investments to Starr Broadcasting Group Inc., a publicly owned company in which he was a a major stockholder. While neither admitting nor denying the allegations, the columnist as part of settlement agreement paid some $1.4 million to shareholders of the company.