The District government, widely praised -- and feared -- for its aggressiveness in ticketing motorists, has failed to follow up and collect $56.8 million in fines and penalties for 2.14 million traffic tickets issued since 1979, a General Accounting Office report found.

The city's Department of Transportation has no reliable system to track down scofflaws because of persistent computer problems, said the report, which was based on examination of tickets written for parking and minor moving violations.

Since 1976, the total worth of uncollected ticket fines and penalties is more than $78 million, the report said. It noted that part of the total was incurred before the city's stepped-up enforcement program began in 1978.

"Some of this revenue may no longer be collectible, but the amount is not known since DOT has not fully implemented policies for writing off uncollectible tickets on a periodic basis," the report said.

During the period covered in the report--1979 through 1981--the department wrote 5.9 million tickets with a face value of $68 million. The uncollected tickets represented $24.8 million in original fines and $32 million in delinquent payment penalties.

The report comes at a time when Mayor Marion Barry is struggling to stave off a projected $110 million deficit due to revenue shortfalls and to city agencies overspending their budgets. Barry is considering a range of program cuts and increased fees or taxes to balance the city's budget.

DOT has said it expects to collect $23.8 million in fines and penalties during the current fiscal year. A DOT official declined comment on the report until his department completes a formal response to the GAO, which is the investigating arm of Congress.

Virginia residents ticketed in the District appear to have benefited most from flaws in the system, the GAO report said. "Virtually no notices have been sent to violators in Virginia for three years" to pay outstanding tickets through May of this year, the report said.

Maryland residents often do not receive pay-up notices for more than a year after the violation, the report said. The District is supposed to send motorists in both jurisdictions notices within 90 days.

D.C. residents, who should receive a notice within 30 days under the DOT regulations, actually get them up to 90 days later, the report said.

In addition, because of computer foul-ups, the city has failed to flag many District residents whose annual registration should be withheld until the fines are paid.

The GAO report was written in September but was not officially released pending a response from the city.

"A major reason for delays in collecting fines is DOT's failure to send reminder notices to violators on a timely and consistent basis," the GAO report said. "Eliminating this backlog is critical because reminder notices are likely to substantially increase ticket revenue . . . . "

The report said that when notices are sent, motorists in 47 percent of the cases pay their tickets, and that 73 percent of those who pay do so within 15 days. "Overall, the data strongly suggests that regular and consistent use of reminder notices would markedly increase both the timeliness and amount of traffic fine collections."

D.C. Inspector General Joyce Blalock is preparing a separate report on the department's failure to collect fines for parking and minor moving violations.

A spokesman for the city said the Blalock report would be completed in a few weeks and would be sent to the mayor, but that such reports generally are treated as internal documents and rarely are released.