The National Weather Service predicted the snowfall in New York would total 14 to 18 inches before ending this morning. The storm, which a spokesman called "a classic nor'-easter," struck only 17 days after New York's worst snowstorm in a decade dumped 13 inches on the city.

Boston was also expecting more snow than 17 days ago. A spokesman for Mayor Kevin White said that extra snow trucks were operating to remove illegally parked cars. They were the city's main snow removal problem during the last storm even though 2,400 were towed.

La Guardia, Kennedy and Newark airports closed in the early afternoon. They were kept open by teams of snowplows for a few landings and departures in the morning. But winds gusting to more than 40 mph in the afternoon made it impossible to keep drifts off the runways.

New Jersey Turnpike officials hired private contractors to augment their force of 250 plows, and dropped the speed limit to 35 mph on the southern half and 30 mph on the northern half.

Hotels in Manhattan and around New York's airports were jammed with strandard travelers by early afternoon.

The New York and American Stock exchanges closed at 2 p.m. after very light trading.

In Trenton, downtown streets were closed to all traffic except emergency vehicles. The state legislature canceled its session and state employes were sent home early. Snow was more than six inches deep in most of the state with record drifts reported in some seacoast communities.

Major snarls began at Grand Central Station when the Harlem, New Haven and Hudson lines lost power in mid-morning, halting all service and stranding trains. Diesel locomotives towed the six to Grand Central but thousands of people had already begun arriving at the station to make their early exit from the city.

When power was restored, Conrail abandoned its schedules and dispatched trains as rapidly as it could bring them to the platforms and load them. One train was departing about every 10 minutes. All trains were turned into locals making all stops. The Long Island Rail Road also was running only locals.

National Weather Service meteorologists said noreasters are the type of storm that bring the heaviest snow-falls to the East Coast. Storms from the Plains usually have colder temperatures and sometimes stronger winds, but less snow.

The center of this storm was well off the coast, but moved very slowly yesterday, meteorologists said.

In Pennsylvannia yesterday, a tractor-trailer and a bus carrying 46 girls from New York City collided on Interstate 80 near Bloomsburg, injuring 21 of the girls, four of whom were hospitalized. The section of the road where the accident occured was closed at midmorning because of the weather.

State Department of Transportation crews, trying to salt the streets in Philadelphia, which had six inches of snow by noon, were forced to halt at 10 a.m. because they could not get around cars and other vehicles stuck in the snow.

In Connecticut, the snow began about 3 a.m. and more than four inches had accumulated in parts of the state by midmorning. Part of the Connecticut Trunpike was closed because of a three-car accident, and travel on other roads was restricted.

In Massachusetts tides were expected to be two to four feet above normal during the snowfall and forecasters warned of flooding dangers.

While the storm was battering the coast, however, Oswego, N.Y., on Lake Ontarlo was getting a respite.

Oswego had had more than 120 inches of snow by Jan. 22, but Mayor John Fitzgibbons said yesterday there hasn't been any new snow and the forecaster on the city payroll doesn't predict any.

Elsewhere in the nation:

A snowstorm off Lake Michigan dumped heavy snow on northern Indiana. Schools closed in Gary. Chicago expressways were slick after an overnight snow, and residents of St. Louis suffered in a record temperature of 8 below zero.

High winds whipped up ground blizzards on the northern Plains. Nearly 100 travelers took shelter overnight in a school and cafe at Moorcroft, Wyo.

The latest in a series of Pacific storms lashed California, leaving new wind and rain damage. Traffic on Interstate 5 between Los Angeles and Bakersfield was hampered for the second day by a mile-long mudslide that blocked all southbound lanes. Hourslong tieups were reported.