Ordinary differential equation based models find application in a wide variety of biological and physiological phenomena. For instance, they arise in the description of gene regulatory networks, study of viral dynamics and other infectious diseases and so on. In the field of toxicology, they are used in physiologically based pharmacokinetic models for describing absorption, distribution, metabolism and excretion of a chemical in vivo. Knowledge about the model parameters is important in understanding the mechanism of action of a chemical and are often estimated using nonlinear least squares methodology. However, there are several challenges associated with the usual methodology. Using functional data analytic methodology, in this article, we develop a general framework for drawing inferences on parameters in models described by a system of differential equations. The proposed methodology takes into account variability between and within experimental units. The performance of the proposed methodology is evaluated using a simulation study and data obtained from a benzene inhalation study. We also describe an R-based software developed toward this purpose. Copyright © 2013 John Wiley & Sons, Ltd.