We develop an approach to the construction of Lyapunov functions for the forward equation of a finite-state nonlinear Markov process. Nonlinear Markov processes can be obtained as a law of large number limit for a system of weakly interacting processes. The approach exploits this connection and the fact that relative entropy defines a Lyapunov function for the solution of the forward equation for the many particle system. Candidate Lyapunov functions for the nonlinear Markov process are constructed via limits, and verified for certain classes of models. Joint work with Paul Dupuis (Brown University)