The curved surface sliding (CSS) system is one of the most in-demand techniques for the seismic isolation of buildings; yet there are still important aspects of its behaviour that need further attention. The CSS system presents variation of friction coefficient, depending on the sliding velocity of the CSS bearings, while friction force and lateral stiffness during the sliding phase are proportional to the axial load. Lateral-torsional response needs to be better understood for base-isolated structures located in near-fault areas, where fling-step and forward-directivity effects can produce long-period (horizontal) velocity pulses. To analyse these aspects, a six-storey reinforced concrete (r.c.) office framed building, with an L-shaped plan and setbacks in elevation, is designed assuming three values of the radius of curvature for the CSS system. Seven in-plan distributions of dynamic-fast friction coefficient for the CSS bearings, ranging from a constant value for all isolators to a different value for each, are considered in the case of low- and medium-type friction properties. The seismic analysis of the test structures is carried out considering an elastic-linear behaviour of the superstructure, while a nonlinear force-displacement law of the CSS bearings is considered in the horizontal direction, depending on sliding velocity and axial load. Given the lack of knowledge of the horizontal direction at which near-fault ground motions occur, the maximum torsional effects and residual displacements are evaluated with reference to different incidence angles, while the orientation of the strongest observed pulses is considered to obtain average values.