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In this paper, we work on the ruled surfaces obtained by aquasi normal and quasi binormal vectors along a spacelike space curve inthree dimensional Minkowski space. Time evolution equations dependingon quasi curvatures are obtained. Studying directional evolutions of bothquasi normal and quasi binormal ruled surfaces by using their directrices,we investigate some geometric properties such as inextensibilty, developability,flatness and minimality of these ruled surfaces.AMS (MOS) Subject Classification Codes: 14J26; 51B20; 57R25KeyWords: Evolution surface, Minkowski space, quasi frame, Ruled surface.