Special to The New York Times.

HAVANA, Jan. 1--A series of small bombs exploded last night in Havana and its suburbs as the public celebrated New Year's.

The bombs caused some alarm but no injuries and little property damage.

Reports of heavy fighting between the insurgents led by Fidel Castro and Government troops near Niquero and Manzanillo, in Oriente Province, have reached Havana.  One report said a large contingent of rebels had attacked several hundred troops near Niquero and inflicted heavy casualties.

It was said that a group of rebels had seized the airport at Manzanillo and that a sharp battle had taken place with troops from near-by army camps before the rebels were driven off.

Both Niquero and Manzanillo are near the Sierra Maestra, the stronghold of Senor Castro and his insurgents.

Camp Columbia army headquarters here said tonight, that eight rebels were killed last night in an encounter with Government troops at Minas Buey Arriba in the Sierra Maestra.  Government troops suffered no casualties, army headquarters added.

In Havana, a bomb exploded in the grounds of the National Capitolio as crowds celebrated bomb in near-by sidewalk cafes.  A bomb damaged electric power installations and blacked out a portion of the Vedava residential district for more than an hour.

The bombs reduced somewhat the attendance at night clubs, cafes and caparets, but in general failed to dampen the public's celebrating spirit.  Streets were crowded and traffic heavy until early in the morning.

In the city of Camaguey, capital of Camaguey Province, military authorities announced that two youths had been killed and three arrested when they attacked a police automobile.  According to the authorities, the group fired on the car, wounding a policeman, and a gun battle ensued.