This article describes a method for representing and simulating ordinary differential equation (ODE) systems which are imprecise - that is, where the ODE model contains both parametric and functional uncertainty. Such models, while useful in engineering tasks such as design and hazard analysis, are not used in practice because they require either special structures which limit the describable uncertainty or produce predictions which are extremely weak. This article describes SQSIM (for SemiQuantitative SIMulator), a system which provides a general language for representing and reasoning about many common forms of engineering uncertainty. By defining the model both qualitatively and quantitatively and by using a simulation method that combines inferences across the qualitative-to-quantitative spectrum, SQSIM produces predictions that maintain a precision consistent with the model imprecision.