The 200 Roman Catholic bishops who will gather at the Vatican today for the Synod of Bishops face one of the most formidable tasks in recent church history: bridging the gap between what the church teaches about family life and what millions of Catholics practice.

Over the next month, the bishops and their corps of advisers will address some of the most vexing questions facing Catholics today: birth control, divorce, the changing role of women and sex outside marriage.

In anticipation of the synod, the Rev. Andrew Greeley and his staff at the National Opinion Research Center conducted a study, reported in the Sept. 27 issue of America magazine, which they describe as "a profile of the present condition of the American Catholic family."

Earlier NORC studies have documented the large number of practicing Catholics who use artificial contraception despite church teaching against it. cAnd the number continues to grow.

The survey found that only 4 percent of Catholics in their 20s support the church's teaching against contraception. Of Catholics in their 20s who go to mass every week, only 13 percent believe contraception is wrong.

On other issues, 11 percent of Catholics in their 20s believe that divorce is wrong and 17 percent believe that premarital sex is wrong. Both practices are condemned by the church.

"There is very little support, even among weekly communicants, for the church's teaching on birth control," Greeley and his associates observe.

The average number of children that Catholics of all ages feel is ideal for a family was 3.2, according to the study; Catholics in their 20s and 30s put the number at just under 3.

The study found that nearly 1 percent of those under 30 not living alone live with a member of the opposite sex to whom they are not married. They "think that 'living together' simply is not wrong," the NORC team stated.

While Catholics in such a situation do not attend mass regularly -- only 1 in 20 recieves communion weekly -- "they do not seem alienated from the church," the observers say. "They are as likely as the young marrieds to see themselves as close to the parish, to value the identity and meaning . . . of Catholicism, to want to pass its world view on to their children and to engage in Catholic activities such as retreats, days of recollection, talking to a priest about a religious problem, and participating in discussion groups," the social scientists said.

The study reported that 18 percent of all Catholics have been divorced. The figure may not reflect the true picture since some Catholic divorcees, barred from the church's sacraments if they remarry and sometimes ostracized by fellow Catholics for violating church law, will leave the church.

The Greeley study suggested that the church faces serious problems over the role of women. "About one third of young Catholic women may be said to be deeply disturbed by the church's perceived position on the role of women, and another one third are distinctly unhappy with it, "the researchers stated."

Greeley and the others state that the question of ordaining women to the priesthood "seems to be important symbolically," particularly to Catholic women under 50. With the church precluding further discussion of this question, "one cannot be hopeful about the prospects for dialogue with many of these young women," the researchers warn. There has been considerable discussion of the synod at a number of levels in this country so that the five American bishop-delegates and their advisers would be informed on the situation here.

Dolores Leckey, the first lay woman to serve as a perita, or expert adviser, to a Synod of Bishops, said she hopes that "what will be initiated will be a dialogue between married people, bishops and theologians, so that there can be developed a theology of marriage and family."

She said she doesn't think the synod will mandate any changes in church laws, but that "the context for study of a lot of questions is likely to be enlarged."

There is a lot of talk, said Leckey, who coordinates work with lay people for the U.S. Catholic Conference, that what may come out of the synod is the beginnings of a "theology of sexuality. . . of how we know God through sexuality; how we know God through intimacy."

Such studies could ultimately affect church policy, she said. "If the bishops can be brought to looking at things in a new way, then in the long run it can have a very immediate affect on the average Catholic."