A TOUGHER federal fair housing bill passed the House in 1980 but was killed at the end of the session in the Senate. In 1983 hopes were raised when bills were sponsored by HUD Secretary Samuel Pierce and Sens. Charles Mathias and Edward Kennedy. But instead of seeking compromise, some advocates of the senators' bill denounced the administration bill, and neither measure advanced.

The argument was over an important question -- how to provide speedy and effective relief for people unable to buy or rent because of racial, religious or sexual discrimination. There was something to be said on both sides. But now Sens. Mathias and Kennedy have introduced another bill, which goes some way toward splitting the difference, and Sen. Robert Dole is about to come forward with a similar bill supported by Mr. Pierce and the administration.

The differences between the two bills have been narrowed. The Kennedy-Mathias bill again provides for hearings and decisions by administrative law judges on discrimination complaints, but it drops the fair housing review commission in the 1983 bill and makes the administrative law judges' decisions appealable to the federal courts. This gets closer to the administration's 1983 version by eliminating an extra layer of judges, and seems to provide for speedier enforcement. The Mathias- Kennedy bill also has high fines, as the 1983 administration bill did. The administration bill now has enforcement by administrative law judges.

Opposition is likely to come from the National Association of Realtors, which opposed Mr. Pierce's decision last year to spend $4 million on using testers to investigate discrimination. The NAR has a lot of members around the country and is one of the biggest campaign contributors in town.

But is it really in real estate agents' interest to oppose these measures? There has been a sharp increase in private fair housing lawsuits lately, with verdicts as high as $560,000 for acts of discrimination. It would be preferable for everyone to provide complainants with a fair, speedy procedure rather than force them to rely on lawsuits that in some cases might ultimately bring big awards but would also delay the one thing the complainant most wants -- the housing of his or her choice.

The remaining differences between the Kennedy-Mathias and administration bills do not appear great, and their basic goals and approaches are similar. The important thing is to move ahead. Thousands of Americans are still encountering discrimination and unfair treatment in their search for homes. A stronger fair housing bill can make a difference. The Senate Judiciary Committee should hold hearings so that the Senate, which blocked the 1980 law, and the House, which passed it, can act this year.