This research focuses on the evaluation of the seismic response of three doubly symmetrical RC wall structures having three height regimes and subjected to a series of bi-directional ground motion recordings. The recorded strong ground motions are rotated in a clockwise direction and the effects of this procedure on several engineering response measures (e.g., wall-bending moments, wall shear forces, and storey drifts) are evaluated. The three doubly symmetrical RC wall structures are designed according to the current Romanian seismic design code for a peak ground acceleration of 0.25 g. The strong ground motions used in this study consist of five pairs of recordings from the Vrancea intermediate-depth earthquakes of 1977, 1986, and 1990 and from the Erzincan and Aigion earthquakes in Turkey and Greece. The investigations show differences between the response measures as a function of the orientation of the strong ground motion horizontal components and significant differences between the responses of each individual structure, as well. Thus, the maximum response obtained from the rotation procedure can be regarded as dependent on both the ground motion characteristics and on the ground motion recording, as well.