Hurricane Alicia, with winds building to at least 115 mph after it stalled temporarily in the Gulf of Mexico, moved steadily toward the Texas coast early today as residents of Galveston and other coastal cities braced for the impact of what the National Weather Service called "a dangerous hurricane."

Early this morning, the service said that Alicia's winds were strengthening and that the storm would move across the upper Texas coast during the pre-dawn and early-morning hours. "All preparedness actions should have been completed," the report said.

At the time, Alicia, the season's first Atlantic hurricane, was 35 miles south of Galveston, about 20 miles from land and moving generally to the northwest at about 5 mph, with hurricane-force winds covering an area 100 miles in diameter.

By early this morning, 70-mph winds were lashing Galveston, uprooting trees and tossing cars and boats. The city of 60,000 people, 50 miles southeast of Houston, was anticipating tides 12 feet above normal and 10 to 15 inches of rain.

As Alicia moved closer to the coast, it appeared to be heading in a more northerly direction, and weather service officials said it likely would hit closer to Galveston than was thought earlier. Those reports triggered new fears that the damage could be greater than expected.

Thousands of residents in low-lying areas of Texas and Louisiana had been evacuated by late last night, and officials in Texas encouraged others to follow. But most residents prepared to ride out the storm after stocking canned goods, water, candles, batteries and other supplies.

Early today, Galveston Mayor E. Gus Manuel recommended that about 3,000 residents leave two low-lying areas of the city. Galveston opened several schools as shelters and was prepared to open others if more evacuees appeared.

Galveston was the scene of the worst U.S. hurricane disaster in this century, when at least 6,000 people were killed in 1900 by a storm that packed 120-mph winds and raised tides almost 20 feet above normal.

Hurricane warnings remained in effect along 500 miles of the Gulf Coast from Corpus Christi, Tex., to Morgan City, La.

Alicia stalled in the gulf for about three hours yesterday, and its winds increased from 85 to 115 mph during the day, building toward what Weather Service officials said could be a "major hurricane."

Weather forecasters in the area predicted that Alicia could become a major storm by the time it reached the Texas coast, and warned residents that it was turning into "an increasingly dangerous hurricane."

The storm headed toward landfall almost 14 years to the day after Hurricane Camille hit the Mississippi coast, killing 255, leaving 68 missing and causing $1.42 billion in damage.

The Red Cross established 41 shelters in a nine-county area along the Texas coast, and 20 more were placed on standby. They were staffed by more than 500 volunteers. By early evening, about 7,000 people were at the shelters, according to Bill Barron of the Houston Red Cross.

As Alicia gathered strength, state and local officials sparred last night over the necessity of evacuating the coastal areas.

Texas Gov. Mark White met with the state's Emergency Management Council and warned, "A lot of people have been lulled into thinking that this is not a dangerous sort of thing. I am concerned with the situation in Galveston. They should be very careful. We shouldn't wait any longer than absolutely necessary to make those decisions" on evacuation.

Early in the day, Galveston officials advised that residents who wanted to take precautions should leave by 2 p.m. Some heeded the warnings, but many did not.

At the time, Mayor Manuel told Washington Post special correspondent Anna Bennett that he was not ordering an evacuation, and city officials reported that traffic leaving town was no greater than normal.

"The governor does prefer we be overly cautious, but of course we've had some different experiences," Manuel said. "We've cried wolf, and the wolf didn't come."

Manuel said he believed there was enough shelter on the island for those who wanted to remain there, and explained the relative calm of many residents there by saying, "Two-thirds of our citizens are old-timers."

In Bay City, Tex., near where Alicia was expected to hit first, City Hall was closed in late afternoon and workers were ordered to leave. But Sharon Serafino, secretary to the mayor, said the people taking the greatest precautions were newcomers to the area.

"We're old hands at this," she said. "We were born here and grew up in it. I think we'll make it fine."

Nevertheless, most of the low-lying coastal areas were evacuated.

"There are only a few of them left," Police Sgt. B.J. Whitburn of Jamaica Beach, west of Galveston, told the Associated Press. "Those who are crazy enough to want to stay, we're telling them, 'Okay, give us the name of your next of kin,' because once the flooding starts there's no way they're going to get out."

In Houston, office buildings began emptying in mid-afternoon as the city prepared for heavy rains and predictions of major flooding. Residents stocked food, water and other supplies.

A Red Cross shelter in Lufkin, Tex., about 126 miles north of Houston, was expected to accommodate Houston residents fleeing the expected flooding. Other areas began preparations for rain and floods as far inland as Austin, 165 miles west of Houston.

The storm that hit Galveston in September 1900 brought 120-mph winds for two days and devastated the coastal city, damaging every building. Between 6,000 and 8,000 people were killed. A 17-foot sea wall was later built to catch the brunt of any storm. In recent years, however, there has been considerable development on the western tip of the island threatened by Alicia. The last fatal hurricane to hit Texas was Fern, which struck near Corpus Christi in 1971, killing two people.

Alicia affected two labor disputes yesterday. Striking telephone workers said they would leave picket lines long enough to restore emergency and essential communications, at no pay, said officials of the Communications Workers of America.

Talks in Houston between Continental Airlines and striking mechanics were postponed until Monday.