The flutter-type instability of a two-member cantilever compound column, loaded by a subfollower force and considered as a geometrically non-linear system, is studied. The effect of asymmetry of axial and flexural rigidities and unit masses of both bars, as well as the follower parameter, on the value of the critical force is discussed. The problem is solved using the perturbation method. The results of numerical calculation are compared with those obtained for a single column. The existence of the smallest critical force was observed for a column composed of bars of asymmetric distribution of flexural rigidities.