One in every three college presidents in NCAA Division I say there are some football and basketball players at their schools who do not belong in college, and two out of every three presidents cite commercialization as a major problem in intercollegiate athletics today, according to respondents in a poll by The Washington Post.

Based on the poll, to which more than two-thirds of all Division I presidents responded, proposals for most reforms will receive overwhelming support at this week's special NCAA convention in New Orleans. At the insistence of the 18-month-old NCAA Presidents Commission, which called for the convention, the votes on eight major proposals on issues of institutional integrity will be by roll-call vote for the first time.

In addition, six of every 10 presidents responding favor Proposition 48, and without modifications that have been discussed for 29 months since the rule significantly strengthening first-year athletic eligibility requirements was passed at the 1983 annual convention. It is due to become effective in August 1986.

Proposition 48 requires a 2.0 grade-point average in a core curriculum of 11 academic subjects plus a minimum score of 700 (out of 1,600) on the Scholastic Aptitude Test or 15 (out of 36) on the American College Test to be eligible as a freshman. The test score provision has been controversial, and the support in The Post poll for implementing it without modifications surprised a number of presidents and athletic directors.

The poll showed overwhelming support for reforms across the board in all three subdivisions of Division I: the major football-playing schools (I-A), the other schools that play Division I football (I-AA) and those schools that do not field Division I football teams (I-AAA). The poll also showed problems are not significantly more widespread in Division I-A than Division I-AA.

The Post poll, conducted by telephone the week of May 13, was one of several in recent months asking college presidents about their views on intercollegiate athletics, the image of which has deteriorated in recent years with scandals involving recruiting and academic abuses, drug use and point-shaving.

In the last six months, the University of Florida received the most severe football probation in recent history, there was a point-shaving basketball scandal at Tulane and there have been reports of a grand jury investigation into big-money bookmaking in Memphis that may involve the Memphis State University basketball team, a participant in the Final Four this past season.

Six of every 10 presidents responding to The Post's poll agreed with the decision made by Tulane, at the behest of its president, Eamon Kelly, to drop men's basketball in the wake of allegations of point-shaving, drug use and illegal payments to players last season. The presidents' view contrasted sharply with that of the general public. In a poll of 1,402 Americans by the Associated Press and Media General, only 26 percent agreed with Kelly's decision.

In another survey of college chief executives by the Presidents Commission, 76 percent reported they were very much concerned by the current state of integrity in intercollegiate athletics, 65 percent said they were very much concerned about the degree of institutional control being exercised over intercollegiate athletic programs and 75 percent said they were very much concerned that the public image of higher education might be damaged by indiscretions in intercollegiate athletics.

When asked by The Post whether they have had a problem at their insitution in the past five years in six specific areas, the chief executive officers of one out of every two schools that play Division I football answered yes to at least one of the six.

A total of 192 presidents responded to the poll. Of that number, 32 said there were recruiting violations at their school in the last five years, 13 noted payments under the table to athletes, three noted point-shaving or other gambling-related activity, 37 cited lower standards for athletes, 36 reported drug use and 23 saw disciplinary problems being overlooked.

The presidents of 16 institutions said they currently had a problem in one of those six areas.

"The response to the individual questions support that most presidents don't believe the problems in their own institution are very severe," said Robert Atwell, president of the American Council on Education. "But, naturally, they do believe there are serious problems. So they're going to go to the meeting and vote for the commission's proposals."

The Post's poll asked respondents whether they approved or disapproved of six of the eight proposals that will require roll-call votes in New Orleans. Of those, only the proposal for an outside audit of all expenditures related to athletics failed to gain at least an approval rate of 85 percent. Only 62 percent of the presidents responding said they favored the outside audit; many of those who opposed it said they already had internal audits and outside ones would be an unnecessary expense. In six of the nation's largest conferences, however, the outside audit was favored, 33-3.

Ninety percent approved of a proposal setting uniform penalties for violations, including abolishment of the affected program for universities caught cheating within five years of a previous penalty. Ninety percent also believe sanctions imposed on a coach should be applied even if he moves to another school.

Ninety-two percent approved of reporting data to the NCAA for freshmen, 88 percent approved reporting to the NCAA the academic status of athletes beyond freshman status and 85 percent approved of reporting graduation rates to the NCAA. None of that data would be made public. But the NCAA would distribute it to its members, without individual schools identified, but grouped as public/private, by enrollment and by geographic region.

In on-the-record interviews with the presidents, there also was support for declaring ineligible athletes who are found in serious violation of NCAA rules. There is a resolution on the agenda in New Orleans directing the NCAA Council to develop such a proposal to be voted on at next year's annual convention.

The Post's poll also showed:

Almost two-thirds of college presidents favor freshman eligibility, although that margin is barely 5 to 4 among the biggest schools playing Division I football.

Three out of 10 said their schools have drug testing, compared to 1 in 7 of the smaller football schools and 1 in 10 of the basketball-only. Of institutions with at least 6,000 enrollment, almost one in every four tests for drugs; in smaller schools, only 1 in 20.

The larger the school, the lower the reported graduation rate for football athletes. In addition, larger schools are somewhat more likely to say some athletes don't belong in college.