Jimmy Swaggart, one of the nation's most popular and powerful evangelists, is under formal investigation by Assemblies of God elders to determine if he has committed adultery, and risks losing his ministerial credentials, according to a source familiar with the probe.

While not confirming the nature of the charges against Swaggart, the Assemblies issued an unusual public statement yesterday that called the matter a "critical situation" that is being handled according to formal church procedures.

Elders of the Assemblies, the same evangelical group that last year defrocked evangelist Jim Bakker for adultery and "alleged bisexual activities," confronted Swaggart over the matter in a four-hour special session Thursday night, according to the church statement.

The Assemblies statement also said the probe is being conducted by officials of the Louisiana district where Swaggart's television empire is based. "Jimmy Swaggart is fully cooperating with the investigation," the statement said.

Neither Swaggart nor his lawyer, William Treeby, was available for comment yesterday. Asked about the charges late yesterday, Swaggart spokeswoman Barbara Klein said: "At this point, we don't have a statement."

The Swaggart investigation is focusing on "sexual moral charges . . . with other women," a source close to the Assemblies said. The probe is believed to have been triggered by evidence presented by Marvin Gorman, a rival New Orleans televangelist, who last year filed a $90 million defamation suit accusing Swaggart of spreading false rumors of sexual misconduct against him.

ABC's "World News Tonight" yesterday reported that Gorman presented Assemblies elders with photographs of Swaggart that supposedly show him visiting a prostitute. But a church official said the pictures were "open to interpretation," the network reported.

Gorman could not be reached last night. One of his lawyers, James Frasier, said representatives of Gorman would soon make a formal public announcement about the Swaggart matter. Asked if Gorman would publicly release evidence that apparently was presented to the Assemblies, Frasier said, "That is a decision we will be making."

A source familiar with the charges said last night that the Swaggart investigation "could have far greater impact" on evangelical Christians than last year's PTL scandal.

The 52-year-old Swaggart, whose television broadcasts reach an estimated 9 million viewers in the United States, is a spellbinding preacher whose revivalist crusades have attracted followers around the world. Last week, 40,000 came to hear him speak during a closing rally in Managua, Nicaragua. From his Baton Rouge, La., headquarters, he operates a $156-million-a-year global television empire, a 1,000-student Bible college and a 7,000-seat church.

Last year, Swaggart helped bring to public light the PTL scandal involving Jim Bakker's confessed sexual encounter with Jessica Hahn. Bakker last night said the new reports about Swaggart were "most confusing and hurtful." He added: "I'm shocked. What we've gone through no one on earth should have to go through." A spokesman for a leading televangelist yesterday said simply, "It's unbelievable."

Juleen Turnage, secretary for information for the Assemblies of God, would not elaborate on the allegations against Swaggart. Depending on the outcome, she said, Swaggart could be stripped of his ministerial credentials or placed on suspension and ordered to submit to a special two-year "rehabilitation" program. If the charges are proven false, she said, Swaggart would be formally exonerated.

The Swaggart-Gorman rivalry stems from a bitter July 1986 confrontation over allegations that Gorman had committed adultery. When the feud first erupted, Gorman acknowledged that he had confessed to Swaggart to having once committed adultery with one woman in 1980. But Swaggart accused him of lying at the meeting, charging that he was aware of signed statements by at least two other women who claimed to have had sexual liaisons with Gorman.

Two months after its investigation, the Assemblies of God defrocked Gorman for "immorality and conduct unbecoming to a minister," according to a church official. He was one of 150 Assemblies of God ministers who are disciplined every year, the official said. There are about 30,000 ministers in the Assemblies of God denomination, which claims 16 million members worldwide.

A Louisiana judge last September dismissed the Gorman defamation suit against Swaggart, saying it was a religious dispute that did not belong in court. Gorman lawyer Frasier said last night that the ruling is being appealed.

Shortly after the dismissal of his lawsuit, Gorman's organization, Marvin Gorman Ministries, filed for bankruptcy reorganization, claiming debts of more than $2 million. He is now the pastor of the Metropolitan Christian Life Church in Metairie, outside New Orleans.