OAKLAND — BART trains are running this morning after the transit system’s unions and management negotiated through the night, averting a strike.

Negotiations continued past the 11:59 p.m. strike deadline, though no deal is in place. At about 5:30 this morning, federal mediator George Cohen said both sides were taking a break and will be returning to the bargaining table this afternoon.

At about 1 a.m. Cohen said both sides had made “substantial progress” but declined to elaborate. It was unclear whether another strike would be threatened for Wednesday or later.

“We apologize (that) the Bay Area continues to have to wait until the middle of the night to find out if union leadership will allow the trains to run each morning,” BART said in a statement early Tuesday. “We hope we can get this situation resolved quickly so the uncertainty can come to an end.”

At 5:35 a.m., Cohen announced both sides were taking a break for a few hours.

Management and BART’s two large labor unions faced an 11:59 p.m. deadline that came and went. An hour later, Cohen emerged from the closed-door talks with the good news for hundreds of thousands of sleepy commuters who had stayed up awaiting word of a possible strike.

Unions had continued to threaten a strike throughout the day. Later in the night, however, the unions had presented a last-second counter-offer that management was reviewing. Details of the proposal were kept under wraps, but Pete Castelli, executive director of the local Service Employees International Union, said: “We did make movement.”

The unions had refused to entertain BART’s final “take-it-or-leave-it” offer submitted Sunday. And BART Board President Tom Radulovich said the agency would not cave: “The money is not going to change,” he said. “We’ve been at this for 150 days at this point — and we think it’s time for the union leadership to let us know, to let the people of the Bay Area know, whether they are going to take an offer to their membership.”

That appeared unlikely. Josie Mooney, chief negotiator for the union, described BART’s final offer as a deal breaker and showed no sign the unions would budge.

Meanwhile, AC Transit on Monday morning submitted a 72-hour notice of a strike for Thursday if a deal was not reached before then. A double-strike later this week would strand 300,000 people who ride BART and AC Transit round trip each day — or 8 percent of all Bay Area commuters, setting up a traffic nightmare of epic proportions.

“It’s the worst of all possible worlds,” said John Goodwin, a spokesman for the 511 traffic service.

The AC Transit strike threat came as a surprise after the bus line and its union twice came to tentative agreements after their contract expired at the end of June. But bus drivers and other union members rejected both deals.

Union president Yvonne Williams said workers are particularly angry about what she described as management’s proposal to increase health care contributions to 10 percent, which would cost $283 a month for some families, she said.

“The bottom line is, it’s the will of the workers” to walk out, said Williams, adding it was a “coincidence” the strike was happening at the same time as the BART labor strife. “The members have spoken loudly and clearly. We do not take this action lightly.”

AC Transit carries 100,000 people round trip each day and was expected to carry the bulk of the displaced riders during a shutdown of BART, which 200,000 people ride round trip each day.

An AC Transit spokesman did not return messages seeking comment.

Meanwhile, the main event — the BART drama — was dragging on Monday after more than six months of talks.

BART’s final four-year offer includes a pay raise of 12 percent on top of the current $76,500 average gross pay for BART’s blue-collar workers, which is highest among California transit agencies. Workers’ pension contributions would rise from nothing to 4 percent and monthly medical costs would jump from $92 to $144.

The unions’ most recently-released offer, made public more than a week ago, includes the equivalent of 18.4 percent pay increases, similar pension costs to BART’s offer and $119 monthly for health care.

Antonette Bryant, president the local Amalgamated Transit Union, said when factoring in the higher benefits costs, BART’s offer amounts to about a 1 percent net raise and is actually worse than a offer she said BART made privately Friday.

“These people have no concern for the riding public and we are appalled by that,” Bryant said. “It’s important for us that the public understand that we are being pushed into a position of striking. This has all been orchestrated by BART.”

BART chief negotiator Tom Hock, who is being paid $399,000 as a contractor, was not at the table Monday and was scheduled to speak at a transit conference in Disneyland on Tuesday. A BART spokesperson said Hock was not needed Monday because General Manager Grace Crunican and other top officials were at the table.

Monday night’s showdown, which included the aid of top federal mediators, represented the sixth strike deadline in the past few months and the third in less than a week, leaving commuters in the lurch yet again.

First, unions went on strike for 4½ days at the start of July when their previous four-year contract expired. Then, Gov. Jerry Brown in August exhausted his powers by twice delaying threatened strikes.

When Brown’s 60-day cooling-off period ended Thursday night, the unions just before midnight delayed a decision on a contract for three days. Then late Sunday night, they again pushed the final word on a shutdown back 24 hours.

During a strike, BART would run free charter buses, other Bay Area transit agencies would expand service and Caltrans would enforce carpool lane rules all day on bridges and East Bay freeways.

Staff writers Matt Artz, Denis Cuff, Mark Gomez and Doug Oakley contributed to this report. Contact Mike Rosenberg at 408-920-5705. Follow him at twitter.com/RosenbergMerc.