Texas A&M University courted Michael Kelley last winter with the kind of whirlwind, expense-paid tour of its campus usually reserved for the recruiting of star athletes.

"What they did to recruit me would probably stretch the NCAA recruiting laws," 17-year-old from Dearborn, Mich., said.

Texas A&M got what it wanted and without having to worry about the National Collegiate Athletic Association rules for recruiting varsity athletes. That is because Kelley, no football player, is an academic superstar with a combined college board score of 1520 of a possible 1600.

Today he is an Aggie, studying aerospace engineering on a $3,000-a-year scholarship.

Kenneth Cochrum, a high school football player, Eagle Scout and class president, considered Princeton, which he said was prepared to offer him a scholarship to play football.

But today he's attending the University of Texas at Austin under a $10,000 scholarship in a new program to attract outstanding students.

The University of Texas and Texas A&M, the state's two largest schools, are on a crash course to greatness. Flush with oil money and hungry for national recognition, they are scouring the country for superstar scholars, the best and brightest from America's high schools.

"We want to be a world-class university," said Peter T. Flawn, president of the University of Texas, whose self-declared war on mediocrity has won him widespread approval.

Critics charge that the two free-spending universities are simply trying to buy a reputation for excellence and that addition of a few big names for the faculties will have little effect on undergraduates' daily lives.

Others argue that great faculties attract great students and that what is happening at the two Texas universities parallels what occurred in California several decades ago. That state built a public university system and two preeminent institutions, the University of California at Berkeley and the University of California at Los Angeles, that are still the envy of the academic world.

In a period of economic austerity elsewhere in the country, Texas has benefited from its relatively healthy economy and the influx of many new high-technology companies helping to raise the educational levels of the state and provide outlets for its brightest graduates. The energy generated by aggressive recruitment of faculty and students in Texas has created a growing awareness around the country of improvements that have been made.

Neither school has reached the upper echelon of America's public institutions, but each believes it is on the edge of greatness. "Everybody feels the time is at hand," said Bryce Jordan, vice chancellor of the University of Texas system who will soon become president of Penn State University.

That may be the viewpoint of top university administrators, but some faculty members complain that the vast resources available to the two schools are being devoted disproportionately to business schools and other areas of commerce that have made Texas wealthy.

The faculty members say too little is being spent on the humanities and say they believe no institution can be considered great without a more balanced program.

Texans credited themselves with academic prominence long before the rest of the world noticed. In 1880, framers of the Texas Constitution, being Texans, decided to think big. So they wrote in their historic document that the legislature should establish "a university of the first class."

Last Wednesday, the University of Texas marked the 100th anniversary of the laying of its cornerstone, believing, perhaps for the first time in its history, that it will achieve that constitutional dictum.

Today the university ranks among the nation's best in physics, linguistics, botany and several foreign languages. Its Humanities Research Center houses one of the world's finest collections of literary manuscripts.

Texas A&M has a notable chemistry department, the largest and one of the best engineering departments in the country, and, of course, a national reputation for agricultural research.

But both universities have been better known for football, Texas for its dominance of the Southwest Conference and A&M for its ability to produce teams as stale as an Aggie joke.

Last January, A&M splashed into national prominence by offering Jackie Sherrill a package estimated at $1.5 million to leave the University of Pittsburgh to become head football coach and athletic director. Detractors said that showed A&M's misplaced sense of priorities, and there was speculation that it would demoralize the faculty.

Instead, while Sherrill and his team suffer through a 5-5 season with one game remaining, against Texas Thursday, the university is snapping its suspenders with pride at the attention it is now receiving for its academic improvements.

"Football is only one of the things happening around here," said Robert Tribble, chairman of A&M's physics department. As proof, he pointed to the $6 million upgrading of the university's cyclotron and the $21 million physics and engineering building soon to be constructed.

Tribble has become a headhunter for academic superstars and is bringing A&M a new reputation as a school willing to pay Nobel laureates winners as much as it pays the football coach.

Tribble is trying to recruit Harvard's Sheldon Glashow, who shared the 1979 Nobel Prize in physics, to head a new Center for Theoretical Physics. Money has not been discussed, according to both men, perhaps because these days money is no object for Texas A&M.

"I don't know the dimensions of the package," said A&M President Frank E. Vandiver, who must approve any deal with Glashow. "But I wouldn't be surprised if it is more than the Jackie Sherrill package."

That would include not only Glashow's salary but those of several other professors he brings with him.

"We don't seek a reputation as a big spender or a non-spender," Vandiver said. "We're just looking for the best faculty we can find."

Glashow has visited the campus twice to give lectures and discuss the position. Last month, he was asked how it would feel to make more than the football coach. "I already make more than the football coach [at Harvard]," he quipped.

The University of Texas also pays top dollar for scholars. Last January, Harvard's Steven Weinberg, who shared the 1979 Nobel Prize with Glashow and another physicist, joined the UT faculty. The package that brought him reportedly included a six-figure salary and jobs for several other junior and senior faculty members. In addition, the UT law school hired his wife as a professor.

The recruitment of Weinberg and, earlier, two other noted physicists--John A. Wheeler and fusion theorist Marshall Rosenbluth--has paid dividends. Last week, the prestigious Solvay Conference in Physics was held in Austin, the first time it was held outside of Belgium since the conferences began in 1911.

What compels the Glashows and Weinbergs and Rosenbluths to leave the Ivy League for big and barbarous Texas is a sense of potential.

"There is a very positive attitude that I've seen in Texas, particularly at A&M, where they still believe in a future better than the present," Glashow said. "The feeling is that positive steps in society will be done first in Texas."

Jack M. Rains, chairman of a Houston architecture firm and head of the A&M task force setting new academic goals for the university, said his group is trying to define for A&M a role as a university that will help lead the country to a revitalized economy as a world trader with expertise in technology and agriculture.

He speaks admiringly of the intellectual "sparks" thrown off by the Harvards and MITs of the East and said, "That will happen here in 20 years if there is a commitment in this state to make it happen."

Because it is the kid from the wrong side of the tracks in Texas education, Texas A&M appears overly anxious to be recognized for throwing sparks.

"Your reputation generally lags five or 10 years between what you are and what people think you are," said Charles McCandless, interim vice president. "If you can bring in superstars, you cut down the lag time."

Last month, A&M's publicity office alerted the national media to a news conference at which the university would announce a "major breakthrough" in energy research. The next day, chemistry professor John O'M. Bockris announced a new, inexpensive method to produce hydrogen from sunlight. But Science magazine, in a subsequent article about it, said A&M had hurriedly scheduled the announcement to take advantage of publicity given a related development by scholars at another institution.

Bockris "refused to disclose substantive detail about his system pending the filing of a patent application," the Science article said. "The credibility of his claims thus rests solely on his scientific reputation, which is generally acknowledged to be good."

If the style of the universities is sometimes annoying, it at least has gotten the attention of the rest of the academic world. Money has a way of doing that.

Officials of the two universities bristle at the notion that there is anything unseemly about its use of money. "It's far too shallow to say those crass Texans are buying their way to superiority," UT's Jordan said. "Any fine insitution buys its way to superiority."

Nor do they accept the idea that UT and A&M are trying to become overnight successes. Flawn and Vandiver say that they are building on foundations laid by their predecessors two decades ago but that the fruits of that work are only now becoming known to the public at large.

Speaking of the recruitment of Weinberg, Rosenbluth and Wheeler to the physics faculty, Flawn said, "We could not have attracted them with any amount of money if we had not built up the infrastructure."

Still, money talks, in academia as in the world of college football, and no one at UT or A&M would be able to think in such grandiose terms were it not for 2.1 million acres of land in West Texas once thought to be virtually useless but now producing a bonanza of wealth from oil and gas production.

The money pumped out of that acreage goes into the Permanent University Fund (PUF), an endowment now worth about $1.7 billion. By law, the proceeds are shared by the two university systems, with one-third devoted to A&M and two-thirds to Texas. According to an old Aggie joke, the reason for that split is that A&M got first choice.

The PUF cannot be touched, but its investment income creates the Available University Fund. Once used for bricks and mortar, it is now used to supplement faculty salaries, buy expensive equipment and generally improve academic programs at the two schools.

But the public wealth of the two institutions is supplemented by private giving, and here, too, UT and A&M are the envy of many other schools. Private donations have helped UT go from an institution without an endowed faculty position in 1960 to one with more than 450 systemwide today.

A special centennial program to endow new chairs and fellowships has been a dramatic success. E.D. Walker, chancellor of the UT system, said he anticipated the program would attract about $10 million in private donations, to be matched dollar for dollar by the Available Fund. Instead, he now believes it will attract $37.5 million in private money for a total of $75 million, swelling the endowed positions to more than 500.

Texas A&M is just as impressive. Last year, its graduates and others contributed about $40 million, ranking A&M second among public universities.

"There is a fair amount of money in Texas today, and some of it is being spent very intelligently," said Glashow, who might be a beneficiary. "Houston managed to get itself a good ballet company. It probably took money. You can say that's crass and loathsome, but it doesn't strike me as particularly immoral."

In recruiting bright students, the universities are proving equally aggressive. Last summer, Texas invited 1,200 of the brightest high school juniors in the state to spend four days on the Austin campus, hoping that the first-hand experience would help the students to decide to enroll there. The university offered each of them $1,000 to say yes.

To recruit outstanding students, A&M has established several different scholarship systems, many of which provide an almost free education.

The result is that each school now boasts about the number of National Merit Scholars it has attracted. Texas says it has about 420, while A&M says it has enrolled more than 400, including 190 in its freshman class.

Because the oil bonanza may not last forever, there is a feeling on the campuses, especially at A&M, that the schools have only a limited time to reach the level of excellence they seek. Vandiver estimates that they have about 20 years.

"In 20 years, we'll either be proved right or wrong," one A&M alumnus said. "But what the people back East are really upset about is that we're changing the balance of power."