For the first time since the 16th century, cardinals of the Roman Catholic Church are gathering at the Vatican this week for a secret session that will neither elect a new pope nor add new members to their own ranks.

Although the agenda has been kept secret, Peter Hebblewaite, Vatican correspondent for the National Catholic Reporter, says it will deal with four topics:

Vatican finances, including both the problems of balancing the budget of the 700 million-member church, and, for the first time in the church's history, the possiblity of a public look at Vatican finances.

An evaluation of the first 12 months of the papacy of John Paul II.

Discussion of the role of the Rome-based Curia, the central administrative body of the Vatican.

The role of the Vatican diplomatic service, with special attention to the situation in China, the Soviet Bloc countries and Nicaragua.

Ever since Pope John Paul II called the extraordinary gathering of the church's cardinals last summer, speculation on the purpose of the meeting has preoccupied Vatican watchers.

In recent centuries, the only canonical function of the College of Cardinals has been the election of a new pope on the death of the incumbent.

But in the two conclaves which met in rapid succession last year -- first to choose a successor to Pope Paul VI and a little more than month later to choose Polish Cardinal Karol Wojtyla to succeed John Paul -- I the present pontiff was said to be impressed by the value of the exchange of the cardinals.

Both times before the formal papal conclave began, princes of the church from all over the world met together informally every day for several hours. In the course of discussion of the matter at hand, views and information on the state of the church worldwide were exchanged. The man who is now pope was said to be impressed with these exchanges.

As Cardinal Wojtyla, he had played an important role in the only world-wide consultative body existing in the church: the Synod of Bishops, mandated by the Second Vatican Council and held every two or three years.The next synod meets in 1980.

Churchmen who served with him on the continuing committee for the synod report that he has a deep commitment to collegiality -- the sharing in the decision-making in the church between pope and bishops -- also called for by Vatican II.

Thus in midsummer when he summoned the cardinals to the secret meeting, there was speculation that he intends to turn the heretofore largely honorary rank of cardinal into a second working consultative body.

Other than a brief announcement that the cardinals would meet for an "examination of current issues," the Vatican has kept details of the meeting secrets, but mailed each cardinal an agenda setting out the points for discussion in general terms, the Associated Press reported from the Vatican.

[Some observers believe the pontiff has set the stage for potentially explosive debate, particularly over the Vatican's finances.]

Sources said it is likely that the pope may ask the richer dioceses in the United States and Western Europe to take on a greater burden of financial help, and in return disclose to the cardinals at least part of the Vatican's financial position.

"If the pope wants their help he'll have to make some disclosures," said one source, who asked not to be named.

For all the secrecy that shrouds Vatican fiscal matters, it is well known that the church for some years has been hard pressed financially. In 1975, the problem became so serious that Paul VI set up a special commission of experts to try to cut expenses.

Inflation, financial losses reportedly in the millions and the fact that much of the Vatican's wealth is not in liquid assets, all contribute to the financial pressures.

The largest item in the Vatican budget goes for salaries, even though salaries at the Vatican are low by secular standards. Nevertheless, just before he left for his American tour, John Paul was confronted by an unprecedented public demand of Vatican employees for a salary increase to cope with Italy's rising living costs.

The role of the Curia, the bureacratic structure that actually runs the Vatican, has continued to be a major question for the church.

The power of the Curia was reduced somewhat by Vatican II and reforms instituted by Paul VI. But the question still remains: to whom is the Curia accountable?

There have been efforts, thus far unsuccessful, in the Synod of Bishops to require heads of the curial congregations and departments to report regularly on their policies and activities to the synod.

John Paul II, who came to Rome as a foreigner unfamiliar with the inner workings of the Curia has yet to make much of an impact on this bureaucracy.