CHICAGO (AP) _ Drug cases have clogged urban courts, delayed civil matters, overcrowded jails and stirred new debate over the best possible solution - legalization or more judges.

''If you want to look at the largest single cause of caseload glut, drugs are it,'' said Albert Alschuler, professor at the University of Chicago Law School. ''We're having fewer and fewer trials, particularly on the civil side. No one can afford to wait. The system's just become unworkable.''

Much of the impact is on state courts, which process about 97 percent of drug arrests. But the federal system also is feeling the crunch. Consider:

- Drug cases in federal courts increased by 280 percent since 1980, Chief Justice William Rehnquist said last December in his annual end-of-the-year report. He urged Congress to act immediately on a proposal to create new judgeships.

In July, the Senate Judiciary Committee approved a measure to create 77 new judgeships. The bill is pending in the Senate.

- Federal drug cases represented more than 26 percent of new criminal filings, and up to 60 percent in some districts, Rehnquist said. Nearly 55 percent of criminal appeals involved drug offenses, compared with 30 percent in 1980.

- The drug caseload rose by 56 percent in 17 big-city courts between 1983 and 1987, according to a 1989 report, ''The Impact of Drug Cases on Case Processing in Urban Trial Courts.'' Among the major increases: Boston - 175 percent; Jersey City, N.J. - 114 percent; the Bronx borough of New York City - 109 percent; and Oakland, Calif. - 95 percent.

- Drug-related cases made up about a quarter of felonies disposed of in 26 big-city courts in 1987, the report said. It noted that number actually is low because it doesn't count incidents in which drugs were involved but didn't constitute the most serious charge.

The situation has turned even grimmer since then; in Detroit, the percentage of state court drug cases more than doubled from 1987 to 1989, said John Goerdt, the report's co-author and senior staff attorney at the National Center for State Courts.

Drug cases, he added, are ''starting to show up in family courts, in juvenile courts, with abused and neglected kids.''

When courts are stressed, ''nobody can render the same quality of justice,'' said James Fyfe, a criminal justice professor at American University in Washington, D.C. ''We all know the old saw that justice delayed is justice denied. ... Evidence disappears. Recollections grow dimmer.''

Complicating matters, experts say, are new mandatory sentencing laws, leading some defendants to seek trial rather than pleading guilty, adding to the backlog.

In Goerdt's report, jury trials in the 26 big-city courts disposed of only 6 percent of all felonies in 1987.

While some propose more staff, U.S. District Judge Robert W. Sweet in New York last year became the first federal judge to publicly advocate drug legalization. The burden is so great, he said, that in September 1989, no federal juries in Manhattan were available to hear civil trials.

Others who have previously supported legalization include Baltimore Mayor Kurt Schmoke and conservative columnist William F. Buckley.

Regardless of different proposals, experts agree the impact is enormous.

''The taxpayers are spending lots of money to warehouse people in jail,'' Alschuler said. ''(Inmates) are sleeping on floors on mattresses. ... Everybody in the system suffers.''