Abstract: The stability of the climatic solution in two-dimensional energy balance model is theoretically analysed. It is shown that the upper bifurcation of the solution which represents northward shift of the ice edge with increase of solar radiation is stable; whereas the lower bifurcation of the solution which represents southward shift of the ice edge with increase of solar radiation is stable. Since current climate of the earth lies in the upper bifurcation of the solution, so it may be considered as stable.