DETROIT (AP) _ City and union negotiators began another round of court-ordered bargaining Tuesday, and the city's chief negotiator said progress was made toward a wage agreement in the week-old walkout by 12,000 workers.

''We're talking. The process is working,'' Detroit labor relations Director Roger Cheek said after negotiations resumed in the afternoon.

The negotiations among bargainers for the city and the American Federation of State, County and Municipal Employees followed about three hours of informal meetings late Monday.

''I feel that there was progress made last night,'' Cheek said Tuesday morning. ''I can see the light at the end of the tunnel.''

AFSCME spokesman Phil Sparks said the two sides met without state mediator Charles Jamerson, who had been assisting the talks. Sparks declined to characterize the talks or say whether an agreement was near.

''There was a session and some movement occurred,'' he said Tuesday.

Wayne County Circuit Judge Sharon Tevis Finch, who has declined to issue a back to work order for employees who perform essential city services such as trash pickup and water treatment, on Tuesday ordered both sides to meet for at least eight hours and report back to her Wednesday morning.

Lawyers for the city also asked the Michigan Court of Appeals to order the workers back to their jobs, but no date was set for a hearing.

Also Tuesday, Philadelphia and the union representing blue-collar workers reached tentative agreement on a contract, one day after the 12,000 workers ended their 20-day strike.

The accord, announced after six hours of negotiations, provides a staggered, 10 percent wage increase over two years, said Mayor W. Wilson Goode.

The strike, together with one begun simultaneously by some 2,500 white- collar employees, left Philadelphia streets piled with garbage, closed museums, libraries and recreation centers and slowed city paperwork, water- main repairs and other services. The white-collar union settled July 12.

In Pittsburgh, the immediate threat of a garbagemen's strike was averted when Teamsters union negotiators accused the city of bad faith bargaining but agreed to extend their current contract on a daily basis while talks continue.

Teamsters negotiators have already agreed to a wage freeze, and differences now center on the size of truck crews. Currently, a driver and two helpers work on each garbage truck. The drivers are paid $12.08 an hour and the helpers earn $11.15 an hour.

The Detroit strike began July 16 after a labor contract extension expired and about 7,000 AFSCME members walked off the job. About 5,000 employees represented by other unions honored picket lines.

The strike shut down bus service used by 200,000 commuters and halted trash pickup in the nation's sixth-largest city, which employs 18,000 people and provides sewage treatment and drinking water for four million metropolitan residents.

Supervisors staffed some services and six emergency garbage dumps were set up around the city.

The strike was sparked by a dispute over wages. AFSCME demanded a 26 percent increase over the duration of a three-year contract, while the city offered a 2 percent boost during the first year.

City negotiators were reluctant to agree to fixed increases during the final two years, insisting instead on tying wage hikes to the city's finanicial health during those years.