Spectra of perturbations of steady-state current transfer to cathodes of high-pressure argon arcs are computed in the framework of the model of nonlinear surface heating. The following pattern of stability has been established for a current-controlled arc on a cylindrical cathode on the basis of the numerical results and trends derived previously by means of an approximate analytical treatment: the diffuse mode is stable beyond the first bifurcation point and unstable at lower currents; steady-state modes with more than one spot are unstable; the axially symmetric mode with a spot at the centre of the front surface of the cathode is unstable; the 3D steady-state mode with a spot at the edge is unstable between the bifurcation point and the turning point and stable beyond the turning point; the transition between the latter mode and the diffuse mode is non-stationary and accompanied by hysteresis. Theoretical results are in agreement with trends observed in the experiment.