Homotopy continuation methods are applied to the nonlinear problem of approximating a higher-order system by a lower-order rational model, such that the mean-square modeling error is minimized. A homotopy function is constructed which creates distinct paths from each of the known solutions of a simple problem to each of the solutions of the desired nonlinear problem. This homotopy function guarantees that the globally optimum rational approximation solution may be determined by finding all the solutions. A simple numerical continuation algorithm is described for following the paths to the optimum solution. A numerical example is included which demonstrates that the globally optimum model will be obtained by applying this homotopy continuation method. >