In this paper an alternative approach to nonlinear pharmacokinetics modelling has been developed from first principles. This "Unsteady Model" is able to describe the situation whereby one or more independent drugs and their metabolites compete for free attachment sites in liver, tissue, red blood cells etc. The Unsteady model collapses to well-known existing models viz: Michaelis-Menten, Langmuir tissue binding and the linear compartment models, under certain well-defined, limiting conditions. The Unsteady model and its collapse to existing models is derived mathematically and illustrated with simulations. For several reasons the Unsteady model would appear to have many advantages and wide application.