Economic theory indicates the need for nonlinear structuralmodels to study medium-term and long-run dynamic behavior of aneconomy. This paper argues that economic systems can be betterspecified and estimated using differential-equation rather thandifference-equation systems and briefly reviews the estimators ofcontinuous models. This approach of specifying structural models onthe basis of economic theory and institutional structure explicitlyand then testing the underlying hypothesis to verify the structuralform is contrasted with a general-to-specific approach ofsuccessively more restricted VARMAX processes.Previous analyses ofstability about the steady state or fixed pointin phasespace are extended to more general attractors to allowan investigation of complexityin economicsystems. The critical dependence of some attractors, andparticularly strange attractors, on parameter valuesemphasizes the need for consistent, efficientestimation. A structural approachprovides a rigorous alternative to using single time series todetermine whether economic systems exhibit aperiodic or chaoticdynamical behavior.