This paper demonstrates the use of a novel suite of data-based, recursive modelling techniques for the investigation of biological and other time-series data, including high resolution leaf elongation. The Data-Based Mechanistic (DBM) modelling methodology rejects the common practice of empirical curve fitting for a more objective approach where the model structure is not assumed a priori, but instead is identified directly from the data series in a stochastic form. Further, this novel approach takes advantage of the latest techniques in optimal recursive estimation of non-stationary and non-linear time-series. Here, the utility and ease of use of these techniques is demonstrated in the examination of two time-series of leaf elongation in an expanding leaf of tomato (Lycopersicon esculentum L. cv. Ailsa Craig) growing in a root pressure vessel (RPV). Using this analysis, the component signals of the elongation series are extracted and considered in relation to physiological processes. It is hoped that this paper will encourage the wider use of these new techniques, as well as the associated Data-Based Mechanistic (DBM) modelling strategy, in analytical plant physiology.