Two weeks after New York Governor Hugh Carey became the fourth husband of Evangeline Gouletas last April, he discovered what it meant to be out of favor with his church.

He was refused permission to serve as godfather at the baptism of a friend's son. Carey, a lifelong Catholic and father of 14, had been widowed for six years and thus was free to remarry. But by marrying the previously wed Gouletas, he was, in the eyes of his church, living in an adulterous relationship unless and until her previous marriages are annulled by the Roman Catholic tribunal, to which the Careys have applied.

As recently as 15 years ago, seeking an annulment was relatively rare. And winning the decree that permits a divorced Catholic to marry again with the church's blessing was rarer still, except for the favored few.

But the divorce explosion that beganin the 1960s swept through Catholic ranks as it did the rest of the country. And the church, in an effort to deal with such enormous emotional and institutional upheaval, has liberalized and streamlined its annulment procedures.

The result: a seventy-fold increase in annulments through the 1970s, with the rate still climbing. In 1968, 445 annulments were granted; more than 31,000 were granted in 1979, the latest year for which statistics are available.

American Catholics now receive 70 percent of the annulments granted by the Roman Catholic Church worldwide, a figure that some in the Vatican have been eyeing with some misgivings.

"Annulments are no longer the private domain of the wealthy or the well-connected," said LaSalle Caron, a Capitol Hill real estate agent and an active Catholic layman, who obtained an annulment after his marriage ended in divorce. Even with this explosion in annulments, church officials estmate that only 5 percent to 10 percent of those eligible for annulments apply for them.

Simplification of the annulment process began in 1968, when the Canon Law Society developed a set of streamlined procedures that made annulments less complicated, infinitely quicker, and cheaper. In 1970, with the backing of the American bishops, the Vatican approved on an experimental basis what has come to be known as the American norms.

At about the same time, the church began to look at marriage in the light of the secular sciences of psychology and sociology, as well as newly developing theological insights. Grounds for annulments were expanded significantly; some canon lawyers contend that under the new criteria virtually any failed marriage could be annulled.

Under current procedures, tribunals in each diocese seek testimony from both former marriage partners. Either partner can seek an annulment after a civil divorce has been granted, but the refusal of an ex-spouse to cooperate will not block the annulment.

The tribunal asks each former spouse for a psychologically oriented autobiography: ". . . Describe the kind of person you felt your father was; your mother. Wht do you remember of your family life up until the time you were 16 or 18?"

Also required is an intimate history of the marriage: " . . . Describe the wedding. . . . Where did you go for a honeymoon? Did anything unusual occur?"

"How do I know if it ws unusual? I'd never been on a honeymoon before," retorted Joan Peterschmidt of Mount Vernon who found the detailed questionnaire "just too much" and declined to cooperate in her ex-husband's petition for an annulment.

The tribunal also takes the testimony of witnesses designated by the petitioner. A trained psychologist may be asked to evaluate the accumulated testimony.

Then the three-person tribunal -- usually three priests trained in canon law, but trained laymen and women increasingly are being used -- sifts the evidence to determine whether or not a true marriage existed. In 90 percent of the cases being processed today, the tribunal will conclude that because of psychological immaturity of the marriage partners, a true marriage did not exist, and grant the annulment.

"It was difficult," said Lou Salmon of Alexandria, who said that her written answers to the questionnaire came to 39 pages, "but they [the priests on the tribunal] were very compassionate. . . . I found that most of the priests on the tribunal were very concerned about the people, concerned about their lives."

Before the new American procedural norms for marriage tribunals were adopted 10 years ago, an affirmative decision automatically would have been appealed by the defender of the bond -- representing the church -- first to a tribunal in another diocese and then to Rome, with each step absorbing additional time and money.

Under the new norms, the first appeal nearly always is bypassed, and the second is short-circulated by a formal request to the National Conference of Catholic Bishops that the parties be dispensed from the appeal to Rome. Although there have been cases in which the paper work needed tidying up, that request ultimately has been granted in every case submitted to the bishops, according to the Rev. Daniel Hoye, who handles the transactions.

In addition to the new streamlined procedures and broadening of grounds for annulment, there has been a revolution in attitudes toward Catholics seeking annulment. Formerly, said the Rev. Joseph Khoury of Holy Trinity Parish, who works with divorced Cahtolics, "the church took the view that the two parties to a marriage case were to be distrusted, so their own testimony was not given much weight."

Now, he said, the thinking tends to be that "people who come to the tribunal tend to be people who can be trusted . . . if they are brought up in the church, the tend not to lie to the clergy."

The cost of an annulment in the Washington archdiocese ranges from $150 to $175, plus psychologist fees that may run from $100 to $300 for the 50 percent of the cases requiring such expertise, said Patricia Perkinson of the Washington tribunal ofice. Costs in other areas are comparable. There are arrangements available to pay on installments, and, said Bernard Dumais of the Baltimore archdioces, "We have never refused anyone because of inability to pay."

For all the relative ease of getting an annulment today, there remain differences of opinion among divorced Catholics as to whether they want to pursue this course.

For Lou Salmon, the annulment process was both a spiritual and a psychological healing of a deep wound.

"There is so much really heavy guilt that people carry, especially in the church," she said. "Divorce is one of the worst traumas that you can come through. The death of a spouse is bad, but divorce just goes on and on . . . and if you are getting condemnation, if you feel that God hates you, you can make too many wrong decisions."

The annulment procedure "was a forgiving process," she said, adding that she found that " working through the annulment process helped me put [the failed marriage] in pespective. . . . It forces you to face the issues head-on by all the digging [through the cause of the marriage failure] in the face of the grief, then you put it behind you."

She said that the day she was notified that her annulment had been granted, she had the feeling: "Now that's a door that's closed. I can begin a new kind of life."

Salmon, who has not remarried, also believes that her ex-husband's cooperation in the annulment -- "He was happy to help me get it. He told me, 'It's the least I can do for you'" -- has helped them remain in a "frinedly relationship," which in turn benefits their four children.

Caron said that he, too, found the work for his annulment " a very relieving and psychologically reinforcing procedure." At the same time, however, he acknowledged having some problem with the basic premise of the annulment: that the marriage never existed.

"The hardest part is to explain to the kids that they are not illegitimate," he said.

But Joan Peterschmidt will neither seek an annulment nor cooperate in her husband's efforts to get one -- which will not prevent his getting one anyway.

Referring to the couple's six children, ages 11 to 21, who have lived with her since the divorce, she said: "There are certain things you try to teach them," about the permanence of marriage. To say, as she believes an annulment implies, "that all that doesn't apply anymore is something I'm not willing to do. . . . I won't make that statement to my kids that if you want to get out and say [a marriage] never existed, you can."

Like many Catholics who reject annulments, Peterschmidt insists that she and her husband at one time had a valid marriage.

"I know there is no marriage now, but I don't need a piece of paper to tell me that," she said.

For divorced Catholics who, for whatever reason, have remarried without getting an annulment, there exists a detour around the canonical ban against receiving holy communion. It is called the "internal forum," or the "good conscience" solution. The couple sit down with a sympathetic priest, review the reasons for the breakup of the first marriage and their failure to get an annulment, and if they can in good conscience decide to present themselves for communion, they do.

Tens of thousands, perhaps millions, of divorced Catholics resort to this solution, with its unspoken message that "God understands, even if the church doesn't."

While this "good-conscience solution" is widely utilized, it has no formal status in church law. The second marriage still is not officially recognized by the church, and a change in parish priests can bring a strict-constructionist pastor who may refuse them communion.

The only resolution to divorce that is universlly recognized by the church remains an annulment.