Seismic response of structures supported on the sliding systems to bi-directional (i.e. two horizontal components) earthquake ground motion is investigated. The frictional forces of sliding system are assumed to be dependent on the relative velocity at the sliding interface with bi-directional interaction. Coupled differential equations of motion of the structure with sliding system in two orthogonal directions are derived and solved in the incremental form using step-by step method with iterations. The iterations are required due to dependence of the frictional forces on the response of the system. The response of the isolated system is analyzed to investigate the effects of velocity dependence and bi-directional interaction of frictional forces of sliding system. Thest effects are investigated under important patametric variations such as the fundamental time period of superstructure, period, damping and friction coefficient of the sliding system. It is ovserved that the dependence of friction coefficient on relative velocity of system does not have noticeable effects on the peak response of the isolated system. However, if the effects of bi-directional interaction of frictional forces are neglected then the sliding base displacement will be underestimated which is crucial from the design point of view. Further, the bi-directional interaction effects are found to be more severe for the sliding systems without restoring force (i.e. purefriction) in comparison to the systems with restoring force.