As a precarious cease-fire on this island nation's northern tip approaches its second week, there are indications that the separatist Tamil guerrillas have lost support among the Tamil civilians in their stronghold because of the ethnic violence that preceded last week's truce.

During a rare two-day visit by journalists to the northern peninsula of Jaffna, Tamil residents said they wanted the cease-fire to hold in the hope that political accommodation could be reached between the militant Tamils and the Sinhalese, the dominant ethnic group.

"We are glad the fighting has ceased. Our people were getting unnecessarily killed," said the Rt. Rev. B. Deogupinnai, the Roman Catholic bishop of Jaffna and a strong supporter of Tamil equality.

Tamils, about 12 percent of the 15 million population, are mostly Hindus. The Sinhalese, who make up most of the armed forces, are mostly Buddhists. The extremist Tamils want to carve out an independent Tamil nation, known as Eelam, in Tamil-majority areas in Sri Lanka's Northern and Eastern provinces, which include Jaffna.

Under the cease-fire announced June 18, the bloody attacks and retaliation by both the Sri Lankan Army and Tamil militants have stopped. They had left approximately 1,000 persons dead during the past year.

The Army remains behind heavy bunkers here, but has reduced security checkpoints that angered residents and ended the massive military sweeps for "the boys," the name Tamils use to refer to the young militants.

Tamil separatist fighters still seem to control much of the north. Four armed Tamil fighters stopped the car of three journalists less than five miles from a police checkpoint. Once it was demonstrated that a shortwave radio was not a transmitting device, they let the car go with smiles and handshakes and even handed back the radio.

A cease-fire violation was reported Monday in the northeastern district of Mannar. Government officials in Colombo, Sri Lanka's capital, reported that one guerrilla was killed in a fire fight outside a hospital where he and 15 other soldiers were taking another soldier for treatment.

Government officials speculated that one of the smaller of the about 35 Tamil guerrilla bands may have been responsible. The five major groups agreed to honor it.

In Jaffna, a city of 1 million that virtually has been cut off from the rest of the country for a year by the insurgency, the militant fighters appear to have lost their support because of lawless acts that have led to retaliation by the armed forces against civilians, residents said. The insurgents' tactics have included the kidnaping of traders, theft of vehicles, and attacks on the Army.

"The boys" showed their muscle here last week by killing the headmaster of a school who tried to organize a cricket match between his students and Army personnel. The match was canceled after separatist fighters warned against it, but they apparently wanted to underscore their opposition to efforts to normalize relations between citizens and the security forces.

The brutal murder of C.E. Anandarajan apparently further isolated the separatist fighters from the public, which until recently had supported the fight for greater autonomy in Tamil areas.

Bishop Deogupinnai said actions by "the boys" have hurt residents. "They stopped trains" by blowing up the tracks "because they were bringing materials for the military. They didn't care that it hurt the people," the bishop said.

"We are between two fires, the armed forces on one side and the boys. They were both armed. Things were happening over which we had no control," he said. "The boys were mining the roads. If a security officer was killed or wounded, the Army would retaliate -- go into homes, take people out and kill them. They didn't get the boys. The people affected are the innocent people."

"Now the militant groups have to change and be satisfied with some sort of autonomy, which the political parties were wanting but couldn't commit themselves [to] because they were afraid of the militants," he said.

The bishop was not the only person here to indicate a cooling of support for the separatist fighters.

Ramalingham Balasubramanian, an attorney and secretary of the Jaffna Citizens Association, said: "By agreeing to end the violence and discuss matters, the Tamils are even now prepared to consider any alternative to a separate state, providing that they do enjoy the democratic rights that an average Sinhalese man also enjoys."

Perhaps the biggest change is that people here are willing to talk openly about excesses by Tamil guerrillas as well as by the government.

A shop owner, Shunmugam Murugesu, first said he had "no problems" with the separatists, but then he acknowledged, laughing, that he had been kidnaped from his house one night last month while his wife and seven children watched.

He said he was taken at gunpoint by six members of the Eelam People's Revolutionary Liberation Front, one of the five major separatist groups, because he had helped arrange the freedom of another trader who had been kidnaped in a business dispute.

While one of his sons went on a hunger strike at a Hindu temple, friends went to another separatist band, the Liberation Tigers of Tamil Eelam, for help in arranging Murugesu's release.