In this paper, two algorithms are presented for the optimum design of geometrically nonlinear steel space frames using tabu search. The first algorithm utilizes the features of short-term memory (tabu list) facility and aspiration criteria and the other has long-term memory (back-tracking) facility in addition to the aforementioned features. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Stress constraints of AISC Allowable stress design (ASD) specification, maximum drift (lateral displacement) and interstorey drift constraints were imposed on the frames. The algorithms were applied to the optimum design of three space frame structures. The designs obtained using the two algorithms were compared to each other. The comparisons showed that the second algorithm resulted in lighter frames.