REMEMBER those cartoons showing platformlike cars being hand-propelled on railroad tracks, with two people seesawing the handles to make the car move along? Well, those cars are self-propelled now, and because of that, they are called ''motorcars,'' or ''speeders.''

The best thing about riding on them is the scenery, says Tom Healy of Belrose, Queens, who keeps his speeder at his weekend home in Woodland Valley in Ulster County. ''You'll go through places you'll never see from a car,'' he said.

On this sunny fall day, Mr. Healy, 42, who works during the week as a yard dispatcher for the Metropolitan Transportation Authority, had met up with Richard C. Wilhelm, 82, of nearby Woodstock, to embark on a motorcar trip along a tourist line called the Catskill Mountain Railroad.

Their starting point was here in Phoenicia at the Empire State Railway Museum, housed in the old station that acts as the depot for the tourist line.

''When you go through some of these small towns,'' Mr. Healy said, ''you're going back in time, getting a real sense of the history.''

The men, each in his own speeder, preceded a small train, packed with camera-wielding tourists, on a short trip along the Esopus Creek at the edge of the Catskills.

Leaving the train behind, the speeders -- which usually travel 15 to 25 miles an hour -- rattled down track bordered by autumnal forest on one side and the roaring Esopus on the other. There was almost no sign of human life.

When the track began to be hidden by brush, Mr. Healy's speeder hit a large tree limb and its front wheels bounced off the track. He and Mr. Wilhelm pulled out extendable handlebars from underneath the car and lifted, righting the car on the track in moments.

''This is why we keep a good distance behind each other on excursions,'' said Mr. Wilhelm, a retired soundman for CBS, adding that he had not heard of any serious accidents involving motorcars.

Motorcar excursions began attracting converts in the 1980's, with the advent of a national group that provided insurance for its members -- thereby alleviating railway companies' fears of accidents caused by unauthorized cars on the rails. The group, the North American Railcar Operators Association, or Narcoa, consists of member clubs that organize trips adhering to a standardized set of safety procedures.

Pat Coleman of Walnut Creek, Calif., Narcoa's president, says the popularity of motorcars is on the rise. But he acknowledged, ''A lot of people just don't realize the hobby is out there.''

From an early enrollment of about 500, national membership now hovers around 1,900; it is increasing at the rate of about 5 percent a year, Mr. Coleman said in a telephone interview.

Also called puddle jumpers or work cars, motorcars were used for track maintenance until the 1970's, when they began to be replaced by Hy-Rail trucks, vehicles fitted with retractable train wheels. But people who loved trains started buying the little engines that could. Informal groups became interested in touring them, but the big stumbling block was getting permission to travel on tracks owned by various rail companies.

The creation of Narcoa obviated that problem.

Walter Rich, president of the New York Susquehanna & Western Railroad, said in a telephone interview that the company allowed rail access to motorcar owners, but only if they applied through Narcoa.

''We try to work with the organized groups so we can accommodate their needs,'' Mr. Rich said. ''And obviously we don't allow them when we have freight operations.''

Each excursion files a travel plan with the company, which provides a ''pilot'' -- an employee in a front car -- for navigation and safety purposes. When another train is scheduled to come along, the motorcars pull onto sidings until the train has passed.

The Susquehanna & Western runs from Secaucus, N.J., to Utica, Syracuse and Binghamton, and is headquartered in Cooperstown. Steve Weiss, a Susquehanna & Western locomotive engineer from Paramus, N.J., is the Narcoa liaison to the railroad.

''A few decades ago you'd be shown the door,'' he said of motorcar enthusiasts' early efforts. ''But with decentralization from large corporations to local companies, they have become much more approachable.''

Mr. Wilhelm and his longtime travel companion Ralph Goneau can attest to that. During a recent viewing of their motorcar in Woodstock, they reminisced about their many adventures together: there was the one they took along coal mine railroads in West Virginia; another on little-used track in Mexico; a third across barren, breathtaking tundra to Churchill, on Hudson Bay in Canada, where the only other mode of transport is atop the ice.

The two extol the virtues of club-sponsored trips, which they take in their spiffy 1975 Fairmont speeder. ''We can go just about anyplace,'' Mr. Goneau said.

The caravans stop each night in a different place and get back onto the rails after a stay in local hotels, he said. And in some places -- like Shamokin, Pa., where the motorcars tool right through the center of the town on trolley tracks -- tourists are agog with questions.

Which only adds to the pleasure.

Photo: Richard C. Wilhelm, in front speeder, and Tom Healy, in rear car, take a trip in Phoenicia using a tourist rail line. ''You'll go through places you'll never see from a car,'' says Mr. Healy. (Photo by Susan Stava for The New York Times)