The shiny new Amtrak Superliner pulled into the tiny station 35 minutes late on its run from Seattle -- a delay that by Amtrak standards is so slight that veteran travelers consider it as good as on time.

Even though Amtrak gradually has extended its schedules to keep its trains "on time," anyone who regularly picks up travelers at the depot knows to call ahead to see when the train is due.

In this case, though, the Amtrak Superliner dashed through a North Dakota blizzard to make up lost time and actually arrived in Minneapolis five minutes early. The passengers, meanwhile, dined on prime rib and stuffed trout that put domestic airline food to shame and watched the snow swirl outside the windows. Afterward, they lazed in comfortable lounge seats, sipped cognac and played cards.

The train is a leisurely way to travel, and by putting its new bilevel Superliner cars into service on its long-distance trains between Chicago and the West, Amtrak is attempting to make it more comfortable.

The Superliners are, in fact, Amtrak's great stainless steel hope. Service on most of the nation's western trains deteriorated significantly after Amtrak was created in 1971 to save the American passenger train from extinction. The Superliner is the first major attempt by the agency to modernize the passenger equipment on those trains.

The Superliners alone elevate Amtrak's Chicago-to-Seattle Empire Builder -- the only train on which the equipment is now in use -- to the ranks of the six best trains the agency operates. The other five are:

The Zephyr, from Chicago to San Francisco, via Omaha, Denver and Cheyenne.

The Southwest Limited, from Chicago to Los Angeles, via Kansas City and Albuquerque.

The Lake Shore Limited, from Chicago to Boston and New York, via Cleveland, Boston and Albany and through some beautiful scenery in upstate New York.

The Metroliners, from New York to Washington.

The Desert Wind, from Ogden, Utah, to Los Angeles over a scenic route.

The Metroliners are simply good, fast transportation in the style of European and Japanese railways. The Lake Shore Limited does not recapture the glories of its predecessor, the 20th Century Limited, but it tops by a long shot any other Amtrak train between Chicago and the East Coast.

The others, by virtue of the beautiful scenery along their routes, are pleasant, leisurely ways to travel as long as Amtrak's heating or air conditioning works in season, the cooks can keep the ancient ovens in their diners working, and Amtrak can keep the trains reasonably on schedule -- give or take an hour.

Amtrak operates some real duds, too -- long-distance trains that should be avoided. They include:

The Panama Limited, the Chigago-to-New Orleans train that often resembles a rolling flophouse. The equipment is frequently dirty, malfunctioning and late.

The Broadway Limited, from Chicago to New York and Washington, which is late more often than it is on time.

The Cardinal, the train between Chicago, Cincinnati and Washington via such places as Hinton, W.Va., and Maysville, Ky. It carries fewer passengers than all but one of Amtrak's long-distance trains.

The Inter-American, the Chicago-to-Houston train, which many Amtrak officials believe should be canceled. The Chicago-to-Houston Lone Star, which was canceled during last year's budget cuts, was a better train.

The Crescent, the Washington-to-New Orleans train that is a shadow of the train by the same name that Southern Railway operated until recently.

The Pioneer, serving Seattle, Portland, Boise and Salt Lake City, which was put into service a few years ago as a political train to mollify western congressmen.

Travel on long-distance Amtrak trains, even some of the worst, can be a pleasant experience as long as there are no equipment breakdowns. Consistency of service remains the agency's biggest problem today, as it was at Amtrak's beginnings nine years ago.

Travelers planning train trips this summer should make reservations as early as possible, especially for sleeping space, because despite significant increases in ridership during the last few years, Amtrak has fewer cars in service now than it did in 1976, when it owned 2,125 cars. It currently owns less than 2,000 units, and only about 1,600 were in service as of Sept. 30.

The 284 Superliner cars that Amtrak has on order were supposed to help alleviate that problem, but delivery of the cars from Pullman Standard Division of Pullman, Inc., has been slow. The only train regularly equipped with Superliner equipment is the Empire Builder.

That train, which traverses some of the most beautiful scenery in the country -- Glacier National Park in Montana and the Cascade Mountains of Washington -- offers a glimpse of what long-distance rail travel could be like in America for the next three decades. l

The bilevel coaches have roomy, high-backed coach seats equivalent to first-class seats on airplanes -- and at half the cost.

The diners, offering meals superior to airline food, or the bland, reheated fare on Amtrak's Amcafe and Amdinette food service cars, provide such entrees as baked stuffed trout at $5.95, strip steak at $8.95 and prime rib at $8.25. A half-bottle of wine with the meal is $2.50, and most drinks are $1.75.

Possibly the best-tasting bargain is the breakfast -- $3.70 for two eggs, sausage or bacon, toast, milk, juice and coffee. The eggs are fresh and cooked to order.

Passengers dine on the upper level of the car. The kitchen is underneath at the track level.

Second-story travel in the Superliner sleepers greatly reduces track noise so that when the train is traveling over welded rail there are no noisy track joints making the clickety-clack sound so familiar to generations of rail-travelers.

Each roomette unit comes equipped with an upper berth that folds into the ceiling -- ideal for children -- and a sliding door that can be locked for added privacy. The roomettes are small but comfortable, although Amtrak has eliminated the toilets in them. Passengers must use the unisex toilets on the first floor.

The larger bedroom units have their own lavatory, an upper berth and spacious seats. (They are available for about 35 percent more than the roomettes.)

Probably the major drawback of the Superliners is that they tend to sway, especially when traveling over rough track. This can be a problem when dining.

Other Amtrak routes probably will not be equipped with Superliners in time for the peak summer travel season. Amtrak has plans to acquire, for $150 million, 150 new single-level coaches and diners for its eastern trains. Bilevel cars cannot be used on those routes because the trains must pass through low tunnels.