In the mornings they come from Philadelphia, Wilmington and Baltimore on this two-car commuter train -- the three-piece-suit set, important people bound for important meetings.In the late afternoons, the four northbound coaches fill with the clerks and secretaries of Washington's vast bureaucratic army.

Given the Chesapeake's timetable coming and going, it could hardly be otherwise: This train arrives in Union Station too late in the morning for most civil servants, and leaves for points north too early in the afternoon for the movers and shakers.

The two traveling societies come from different worlds and, while in Washington, go their separate ways. What they share, unknowingly perhaps, is a train whose separate identity lies in a name, a schedule, a common crew and matching silver cars.

They ride in spartan coaches with one lavatory for two cars and without reclining seats or snack bars. As allowed, the Chesapeake's lightweight, self-propelled cars travel 100 miles an hour, occasionally providing the high-speed service promised in the timetables.

In less than two years this train -- subsidized by Maryland and Pennsylvania to fill a scheduling gap -- has become an entrenched institution along the 134-mile route. Driven from their cars, several passengers said, by high gasoline prices, a daily average of 654 persons rode the Chesapeake in a recent week -- 56 percent more than a year ago.

Shortly before seven, with the sun still low in the eastern sky, the train emerges from Philadelphia's 30th Street Station, about half full. It is scheduled to arrive in Union Station at 9 a.m., 11 stops and two hours and 18 minutes later.

The morning riders are generally uncommunicative. A few sleep, but most sit deeply engrossed in the financial pages or silently studying significant documents around which, in one way or another, the world may turn.

The other week, the morning contingent included a Philadelphia editorial writer bound for a White House budget briefing, the chairman of the U.S. section of the Canadian-American International Joint Commission, a congressional aide, a Justice Department lawyer, a Quaker lobbyist and a stock exchange courier.

Like Robert J. Sugarman, they often lead lived divided between two cities and united by the Chesapeake. Sugarman, the commission chairman, shares a Capitol Hill town house during the week but spends what days he can in Philadelphia, where his children live.

Michele S. deCrus-Saenz, another passenger, teaches romance languages and medieval history at George Washington University, but lives in a Philadelphia suburb. Each day her husband drops her at the Wilmington station, then continues to his job in Deepwater, N.J., across the Delaware Memorial Bridge. He reverses the ritual at night.

Unlike most morning riders who use the train for occasional meetings she is a regular commuter resigned to daily long-distance travel. "That's the way you hold a job in my field," she said. "It's tough for college professors these days."

In Baltimore she was joined by Ken Reich, an environmental lawyer with the Justice Department who complained that the Chesapeake lacked coffee and "it's hard to find a bathroom, but I'm welded to the system. I'd never drive."

DeCrusSaenz glared angrily at her seatmate, but kept her silence. This is her train, right or wrong.

That morning the Chesapeake pulled into Union Station 22 minutes late, after circuit breakers tripped, two of four motors failed in one car and the train was switched to a 30-mile-an-hour track part of the way.

It had been that way all week for the beleaguered train and its frustrated crew. To make matters worse, Amtrak began distributing one million copies of its new Northeast Corridor and National Train Timetables, freshly printed at a cost of $70,000 but containing incorrect afternoon times for -- what else? -- the Chesapeake.

The morning passengers went off to their important meetings while the crew -- engineman J. D. Harrison and conductors John and Jim Lese, who are brothers -- did the usual during their five-hour layover.

Harrison, 32, who also flies airplanes and wears a flight jacket, went jogging around the Mall. The Lese brothers once took the Metro subway to Silver Spring to go bowling. But, mostly when in Washington, they eat and sleep.

At Michael's Restaurant inside the Amtrak building, they greet Shirley the manager, Viv the waitress, Pierre the maitre d' and Paul the waiter. John invariably orders a "western omelette without the eggs," just diced green peppers, onions and ham. They sack out in an inelegant hotel a block from the Union Station where Amtrak rents 25 rooms. By 3 p.m. they are back at Michael's for lunch. by 4 they are on their way again to Union Station.

Then, while the big shots are still meeting, the government secretaries, clerk-typists, Government Printing Office machinists and others who work in Washington, but can't afford to live there, board the Chesapeake.

"You get more money working in Washington," explained Sue Wiggins, the sole support of her family and a commute from Odenton, near Fort Meade. "Without this train, I couldn't do it."

"If I drove, I'd have parking, gas and most of all aggravation," said her companiuon, Mark Emory, a printing specialist with the National Credit Union Administration. Ray McKelway, a GPO machinist, nodded aggreement. He had given up car-pooling from Baltimore County and moved to Hanover, south of Baltimore, to catch the train. For the round trip, the Odenton commuters pay $49 a month.

Their lives are inseparably attached to the regularly shceduled northbound Chesapeake, so much so that an official attempt to move up its departure time by 20 minutes sparked a torrent of angry letters, petitions and testimony at a recent hearing, and finally, a stategic retreat by the decision makers, who settled for a five-minute shift.

Under the new schedule, which went into effect this week, the train leaves at 4:45 p.m.

As the Chesapeake pulled out of Union Station the other afternoon, one rider confided to another, "I have been, as the saying goes, interfacing very closely with the permits division."

Most afternoon conversation, however, is less bureaucratic and more basic after a day's work: "Hi, Kathy. Flat tire on the subway?" a rider asked a late arrival. "Hi, Theresa. Hi, Denise. Enjoy your weekend?" he said, distributing a six-pack of beer he carried with him to his fellow travelers.

The afternoon ride is a relaxing respite from responsibilities of work and home. As the Chesapeake appeared to slope to one side with the roadbed at Lanham -- known among commuters as "the Lanham lean" -- a long-running pinochle game was going strong in the smoking section among Baltimore-bound riders who met aboard the train.

"We can't afford to play for money," said Kitty Ross, who works for the Army. "We spend all our money on transportation," added Denise Ward, a computer programmer with the Veterans Administration.

Back in the front end of the third car can be found a group of young women -- government workers -- who sit in the same seats each night. On Fridays, they bring wine and cheese and crackers and party from Washington to Odenton, where more than 150 riders spill out each afternoon into a crowded station parking lot.

The other Wednesday, the party people brought a bottle of sweet red wine two days early and assistant conductor James Lese, 28, contributed a bag of garlic bread he bought in Washington.

"I made it," he told them as he punched their tickets.

"He made it," four young women said in unison.

"Is the conductor married?" one asked after Lese had walked away. The train crew's on-board life is like that, especially in the afternoons, wrapped in a kind of masculine mystique that adds to the romance of railroading.

"I'm glad I have a conductor that looks out for me," confessed Betty Venvetti, after she repeatedly attempted to get off the train one stop too soon. "Why do I think it's Baltimore all the time? I can't imagine why I do that," she said as conductor John Lese, 38, helped her back on board.

"She does that every night," he shrugged. "Every night, I gotta grab her and put her back on the train."

The last of the throngs emerge in Baltimore, where two of the four homebound cars are left behind and the remaining two proceed almost empty.

John Lese walks through what is left of his train, gently placing discarded newspapers under the raised feet of dozing passengers.

Just above Baltimore near a signal tower they call Petticoat Junction, the train sat still, waiting for a sleek Metroliner to pass. But the powers that be, anticipating snow, had replaced the self-propelled high-speed luxury cars with Amfleet coaches pulled by a vintage locomotive.

The Chesapeake would have to follow dutifully behind.

By Edgewood, the train was six minutes late. But after Newark, Del., the train made up the time. There were no speed restrictions and all signals were up -- "a good piece of railroad," Jim Lese said.

The Chesapeake arrived in Philadelphia shortly after 7 p.m., depositing 14 passengers right on time.

"This is the little train that could, if they let it," John Lese said. The next morning, they didn't: The train rolled into Baltimore 22 minutes late, under a carpet of snow, and the very important passengers had to be bused to Washington because of a freight derailment.