On Thursday, the State House of Representatives gave a narrow 116-110 majority to a bill which may challenge President Nixon's power to wage undeclared war in Vietnam.

According to the bill, a Massachusetts serviceman could refuse to serve "in the conduct of armed hostilities" since there has been no declaration of war by Congress.

If ordered by the Federal Government to Vietnam, a soldier could inform the state attorney general. The attorney general would then appeal the order to the Supreme Court, forcing a decision on the constitutionality of the President's conduct of the war in Southeast Asia.

The measure will have its final reading today and must again be approved by the House before going on to the Senate.

Rep. Timothy Hickey (D-Cambridge), who voted with the majority, said that today's vote may be very close. "The floor debate on the measure will be very important," he explained. "A single issue could change the outcome."

Richard Cauchi, executive secretary of Citizens for Participation Politics (CPP), a group backing the bill, said that "some veterans' groups have begun pressuring representatives to oppose the bill." According to Cauchi, the CPP is also contacting representatives in an effort to insure that the measure retains its majority.