Student demonstrators stoned and attempted to set fire to the American and British cultural centers here today in a fresh upsurge of anti-government activities that left one youth dead and at least four others wounded.

The student strike appears to be part of a larger offensive under way by both leftists and rightists seeking the ovethrow of the Marxist military government that has been in power since the deposition of late-Emperor Haile Selassie in September, 1974.

Two nights ago, slogans demanding the immediate establishment of a civilian government appeared on walls and banners strung across the city's main street. Others called on the extreme leftist Ethiopian People's Revolutionary Party and the anti-Marxist Ethiopian Democratic Union, the two main opposition groups, to unite in their efforts to unseat the military government.

The current upsurge in opposition activities inside the capital, the strongest in months, appears to be directly linked to recent government military reverses in fighting against Democratic Union forces in northwest Begemdir Province and against the secessionist Eritrean Liberation Front in Ethiopia's nothermost Eritrea Province.

The government has lost four garrisons and three border towns to these two opposition groups in the past three weeks and several others are seriously threatened. It has launched a counter-offensive to retake some of ground lost to the Democratic Union in Begemdir but remains stymied by the far stronger forces of the Eritrean Front.

Several thousand army and police reinforcements were flown to the Begemdir Provincial capital of Gondar this week to deal with the growing threat from Democratic Union forces, which are trying to solidify their position along the Sudanese border before launching attacks deeper insider Ethiopia.

The city remained outwardly calm but extremely tense tonight follwing a day of scattered incidents involving striking students, who carried out hit-and-run attacks on the two cultural centers and held small demonstrations at several high schools.

Army jeeps mounted with machine guns and rifle-toting policemen were patrolling the streets of the capital, but there was no attempt by the students to hold a mass demonstration.

Police and heavily armed soldiers opened fire at three high schools in an attempt to break up student gatherings this morning. The government made no official statement regarding casualties but in one incident a student was known to have been shot dead and four others injured.

No injuries were reported in the brief demonstrations held outside the Amercian and British cultural centers. Groups of between 30 and 90 students first smashed windows with stones and then tried to set fires in the offices, either by pouring gasoline inside the building or throwing firebombs. Neither attempt succeeded.

Pracitically all of the center's ground floor windows were broken during the 20-minute assault, however, a U.S. embassy spokesman said.

Both the American and British centers were closed for the rest of the day following the early morning of incidents.

It was the first time in almost three years that demonstrators have attacked the American cultural center. The students were shouting anti-imperialist slogans and the center apparently was a target because of continuing U.S. support of the Ethiopian military government, which they strongly oppose.

The demonstrations began building up yesterday when high school and university students went out on strike in support of demands for the dismissal of several Ethiopian professors and to show their solidarity with disgruntled university employees.

The sharp increase in anti-government activities has created a crisis atmosphere here in the capital. Yesterday, 3,000 representatives of neighborhood dwellers' associations went to the government palace to ask the military to hand out arms so that they could deal with the "reactionaries" infiltrating the city.

Since last Friday, at least two government officials have been shot dead and two others wounded, reportedly by People's Revolutionary Party assassins.