A T-shirt printed with the message, "Dukakis - He's My Man," helped set the tone for the second debate between Rep. Wayne Owens, D-Utah, and the Republican challenger for the 2nd District seat in Congress, Richard Snelgrove.

The pair's first confrontation, before the Salt Lake Rotary Club last week, turned nasty when Owens pointedly criticized how Snelgrove was portraying his record in Congress.Monday, similar exchanges were fueled by a boisterous crowd at the University of Utah. Even Libertarian Michael Lee, making his first appearance with the other candidates, had his share of applause and jeers.

Nearly 100 students gathered in the campus student union at noon for the debate, some of whom cheered at the mention of the Democratic presidential candidate and chanted, "Duke, Duke, Duke."

That was obviously not the response Snelgrove intended when he presented Owens with the shirt at the beginning of the debate and branded both the congressman and the Massachusetts governor liberals.

And he also appeared to be caught off guard when Owens remarked that Snelgrove's holding a shirt that endorsed Dukakis made a good picture for the newspaper and television photographers gathered.

Snelgrove recovered briefly when he held up another T-shirt reserved for himself bearing the names of Vice President George Bush and Sen. Orrin Hatch, R-Utah.

The two top Republicans on the November ballot are expected to win big in Utah, and Snelgrove is counting on Utahns in the 2nd District also to vote for the GOP candidate in the next race listed - his own.

Although that shirt also drew a cheer from the audience, one voice cried out, "What about Noriega?" a reference to the Reagan administration's dealings with the Panama strongman.

The differences between the three candidates became immediately apparent with the first question, submitted by the Associated Students of the University of Utah. The student government wanted to know how each felt the federal government could help higher education in Utah.

As an advocate of eliminating government involvement wherever possible, Lee said the federal government's role in higher education "has been mainly to screw it up."

Owens, on the other hand, said that the federal government should pay one-third of the nation's education costs and called for more money to be spent on university research as well as student grants and loans.

Snelgrove called the incumbent's position "nonsense" and said control should remain at the local level. He said educational institutions in Utah get back only a few cents of every tax dollar sent to Washington, D.C.

There were similar disagreements on subsequent questions dealing with abortion, the proposed amendment to the U.S. Constitution requiring a balanced federal budget, the nation's involvement in Central America and other issues raised by members of the audience.

As in the previous debate, Snelgrove repeated a theme of his campaign, that Owens' stands on the issues in Utah are different from how he votes as a congressman in Washington, D.C.

He cited what he said was Owens' acceptance of a pro-abortion plank in the national Democratic platform despite his opposition to abortion except in the case of incest, rape or when the health of the mother is in danger.

For his part, Owens repeatedly tried to get Snelgrove to explain some of his responses. He asked whether Snelgrove's support of limiting congressional terms to 12 years meant he did not support Hatch's re-election, since the senator is seeking a third six-year term.