Most well-known time-series methods treat the system as a univariate, bivariate or multivariate 'black box'whose parameters provide a convenient and concise description of the data. This is in contrast to physically based, mechanistic models, whose parameters normally have an identifiable physical interpretation. The present paper describes a unified 'data-based mechanistic'approach to the modelling of dynamic systems from time-series data using continuous or discrete-time transfer function models in the time derivative, backward shift or delta operator. This approach, which exploits recursive methods of parameter estimation, represents a useful compromise between the physically based methods of mechanistic modelling and the 'black box'methods of time-series analysis. It provides a powerful tool for the objective investigation of environmental dynamic systems when time-series data are available for analysis. Its practical potential is illustrated by several real examples concerned with the objective investigation of parallel processes in hydrology and water quality.