SUMMARYA random vibration method is developed for the response analysis of hysteretic structural systems under stochastic twodimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of theeffects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.