This paper presents the nonlinear flexural-torsional vibration and instability analysis of thin-walled column with different mono-symmetric open sections subjected to periodic axial load. Non-linear partial differential equations (PDEs) governing the dynamic instability behavior of the considered sections are derived. Galerkin's method is employed to reduce the coupled partial differential equations to a set of coupled Mathieu equations. The amplitudes of steady state vibrations are determined from the non-trivial solution of Mathieu equations in terms of excitation frequency. Following Bolotin's method, principal instability regions are determined for different mono-symmetric section columns having various boundary conditions. Numerical results for the natural frequencies, instability regions and frequency-amplitude responses for thin-walled columns are presented. Influence of eccentricity, shape of the cross-section and boundary conditions on frequency-amplitude responses and instability regions are investigated.