Summary: A state space model is developed for a system of nonlinear differential equations with observations consisting of nonlinear functions of the state variables. This is applied to modelling gonorrhea transmission in a heterosexual population. Variable transformations are used to keep the incidence rates in the interval zero to one and the unknown parameters in the proper ranges. A refinement of the model allows adaptively varying contact rates. The Kalman filter is used to calculate an approximate likelihood, and nonlinear optimization is used to obtain approximate maximum likelihood estimates.