Cambridge tenant groups suffered a major setback Wednesday when the Local Affairs Committee of the State House postponed until next year its decision on the future of rent controls in the state.

The committee killed 36 bills that would have either extended, amended or repealed a four-year "local option" law by voting to study the matter when the legislative session ends late this year.

Tenants fear that the study might continue through next year's session and past the April 1, 1975, expiration date of the present rent control law. Cambridge and Somerville are among the "middle-sized cities" allowed by the law to impose rent controls.

At least 16 tenant groups in the state plan to demonstrate at the State House next month to urge the committee to reconsider extension of rent controls.

"The study is an excuse for politicians to avoid taking a stand on rent controls before the [November] election, a spokesman for the Cambridge Tenants Organizing Committee said Thursday.

Saundra Graham, chairman of the Cambridge City Council Committee on Housing, said the city "will be in terrible trouble when the law expires," predicting local rents will soar dramatically.

While charging state legislators with "really avoiding the issue," Graham said the Cambridge tenants "need to fight to retain rent controls."

Graham submitted a motion before the city council Monday to encourage the state legislators to extend the rent control law. The move failed, however, when Councilor Alfred E. Vellucci abstained from voting and left the council deadlocked, 4-4.

Vellucci, who has favored controls in the past, said after the vote that he felt "the whole rent control situation" needs to be examined carefully. Legislators at the State House echoed those sentiments Wednesday when they dealt their blow to the tenants.