Real systems are often driven by switching reference signals which affect dynamics and/or equilibrium points. This technical note addresses the computation of upper bounds of the minimum commutation time ensuring stability for switching nonlinear systems. Specifically, we consider the cases of constant and variable equilibrium point of interest, for polynomial systems and for a class of non-polynomial systems. We hence propose upper bounds of the sought minimum commutation time by adopting homogeneous polynomial Lyapunov functions for the former case and polynomial Lyapunov functions for the latter one, which can be computed via linear matrix inequaltiy optimizations for given Lyapunov functions.