In this paper, the problem of stabilizing second-order switched nonlinear systems consisting of two unstable subsystems is studied. We present a method for determining if a switched system can be stabilized. Important results from Differential Geometry have been needed in order to study the stabilization in the nonlinear case. Hence, it is established if there exists a switching law under which the solution of a switched system for a given initial condition converges to the origin. In order to illustrate the results we present several numerical examples. Furthermore, the results are applied to a kind of switched systems of higher dimension.