The FBI and the Federal Trade Commission are investigating a nationwide "career-counseling" firm that has closed its Washington headquarters and four other offices, leaving behind thousands of dollars in claims from disgruntled job-seekers who paid advance fees averaging $5,000.

Energetix Inc., one of the largest career-counseling firms in the country, has grossed an estimated $3 million to $7 million per year offering research, resume writing and advice to thousands of job-hunters seeking professional careers through its offices here and in New York, Chicago, Philadelphia and Atlanta, according to industry analysts.

The company, which closed the five offices in recent weeks and is now operating in Sausalito, Calif., is the subject of numerous consumer complaints to the Federal Trade Commission and to state and District consumer protection officials.

The FBI has begun an investigation into whether Energetix violated federal laws in its national advertising and sales techniques, FBI officials confirmed yesterday. The FTC is also investigating complaints, which have increased since the abrupt closings, according to FTC sources.

Energetix officials testified at D.C. City Council hearings in 1983 against a bill to regulate their industry. Efforts to reach the company's officials by telephone yesterday were unsuccessful.

Most of the consumer complaints about Energetix came from customers who said that they paid the advance fees and that the company failed to live up to its promises of giving them access to high-paying new jobs.

The Better Business Bureau of Metropolitan Washington held arbitration hearings in nine Energetix cases, and all nine resulted in arbitrators ordering the firm to refund between $3,500 and $5,000 of the fees, said BBB operations director Marsha Goldberger.

But Energetix has not paid four of the nine judgments. Last year, the bureau said in an advisory to its members that those were "long overdue . . . , despite repeated promises to honor obligations." The BBB said yesterday that it would no longer handle Energetix cases because of the failure to pay the judgments.

Career-counseling firms -- unlike conventional employment agencies or executive "head-hunting" firms -- get their money from job-seekers rather than from companies, and take fees in advance, rather than after clients find jobs.

But 44 states, including Maryland, prohibit "up-front" or advance fees by employment agencies, and most states specify that the career-counseling firms are included in such bans. Maryland and Virginia have various rules governing career counselors, but Virginia does not prohibit the up-front fees.

The District last October passed a new career-counseling law banning the advance fees and regulating the language used by counselors claiming to offer access to jobs.

It could not be determined whether the District's new law, which took effect March 13, was related to the closing of the Energetix offices here or elsewhere.

Energetix President Michael W. Mergen testified in 1983 that the advance-fee ban would put the firm out of business, because Energetix incurs costs in conducting research, counseling, and resume-preparation before the client can land a job.

George Uhimchuk, a Clemson University economist, who said he paid $3,700 to Energetix, said yesterday he went to the firm because "I needed someone with good contacts in private industry who could help me get interviews."

Uhimchuk said Energetix officials told him they would provide a "tailored mailing list" of companies, and "contacts with the people who could say 'yes' " to a job.

Energetix prepared him a resume, he said, but used outdated and inaccurate mailing lists, sending it to employers who complained of being "flooded" with resumes of Energetix clients, Uhimchuk said.

Instead of job offers, he said, he received letters of complaint from employers asking to be taken off the "mailing list" of resumes.

"It totally destroyed my job search," said Uhimchuk, who said that he retained a lawyer, who forwarded his complaint to the FTC and D.C. officials.

Mergen said in a 1984 interview with The Washington Post that Energetix had a success rate of more than 90 percent in job placements.

Richard Evans, a former senior partner in the firm's Washington office, said yesterday that, to his knowledge, the placement rate was "2 to 3 percent" during his eight months with Energetix, until August 1983.

Evans, now the president of a Kentucky newspaper firm, said, "We would get about 22 clients a month. In the eight months, I know of one person who I could say directly got a job through Energetix" while others may have found jobs through other means.

A spokesman for the New York State attorney general's office said yesterday that the agency is investigating consumer complaints from six Energetix customers seeking refunds because the firm closed on short notice.

Federal prosecutors in Illinois are also investigating the Energetix case, according to federal officials.