The California Building Code requires at least two ground motion components for the three-dimensional (3-D) response history analysis (RHA) of structures. For near-fault sites, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately. This approach is assumed to lead to two sets of responses that envelope the range of possible responses over all non-redundant rotation angles. This assumption is examined here using 3-D computer models of single-story structures having symmetric and asymmetric plans subjected to a suite of bidirectional earthquake ground motions. The influence that the rotation angle has on several engineering demand parameters is investigated in linear and nonlinear domains to evaluate the use of the FN/FP directions, and the maximum direction (MD). The statistical evaluation suggests that RHAs should be conducted by rotating a set of records to the MD and FN/FP directions, and taking the maximum response values from these analyses as design values.