Given a family of linear systems which admit an asymptotically stable convex combination, the existence of stabilising time-dependent switching rules can be proved by using the Baker-Campbell-Hausdorff formula for exponentials. The control laws obtained in this way are periodic, fast switching and independent of the initial state. We prove that under a similar assumption, the approach can be extended to provide stabilising time-dependent switching rules for the families of nonlinear vector fields, as well. However, the resulting control law, in general, is not periodic, not fast switching and it may depend on the initial state.