Economic theory indicates the need for nonlinear structural models to study medium-term and long-run dynamic behavior of an economy. This paper argues that economic systems can be better specified and estimated using differential-equation rather than difference-equation systems and briefly reviews the estimators of continuous models. This approach of specifying structural models on the basis of economic theory and institutional structure explicitly and then testing the underlying hypothesis to verify the structural form is contrasted with a general-to-specific approach of successively more restricted VARMAX processes. Previous analyses of stability about the steady state or fixed point in phase space are extended to more general attractors to allow an investigation of complexity in economic systems. The critical dependence of some attractors, and particularly strange attractors, on parameter values emphasizes the need for consistent, efficient estimation. A structural approach provides a rigorous alternative to using single time series to determine whether economic systems exhibit aperiodic or chaotic dynamical behavior.