State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, the use of state dependent differential Riccati equations and numerical integration to propagate their solutions forward in time. Stability is examined and examples illustrating the use of these methods are given.