Most of the existing approaches to identification of nonlinear dynamic systems involve matching a given input-output behaviour with empirical discrete-time approximations such as artificial neural networks, Kolmogorov-Gabor polynomials, radial basis function networks, etc. Techniques for dealing with physically-based continuous-time models are either applicable to only a restricted class of systems or are computationally very demanding. In this paper a new methodology is presented that is applicable to a large class of nonlinear continuous-time systems, by defining a set of Hartley modulating functions for characterizing the continuous process signals. The advantages of this new class of modulating functions are that a set of algebraic equations with real coefficients results, the formulations are free from boundary conditions, and the computations can be made using fast algorithms for the discrete Hartley transformation. The resulting estimation scheme is applied to different categories of nonlinear systems and is tested under both noise-free and noisy conditions.