A new parametric approach for the study of Lagrangian data is presented. It provides parameter estimates for velocity and transport components and is based on a stochastic model for single particle motion. The main advantage of this approach is that it provides more accurate parameter estimates than existing methods by using the a-priori knowledge of the model. Also, it provides a complete error analysis of the estimates and is valid in presence of observation errors. Unlike nonparametric methods (e.g. Davis, 1991b), our technique depends on a-priori assumptions which require that the model validity be checked in order to obtain reliable estimates. The model used here is the simplest one in a hierarchy of “random flight” models (e.g. Thomson, 1987), and it describes the turbulent velocity as a linear Markov process, characterized by an exponential autocorrelation. Experimental and numerical estimates show that the model is appropriate for mesoscale turbulent flows in homogeneous regions of the upper ocean. More complex models, valid under more general conditions, are presently under study. Estimates of the mean flow, variance, turbulent time scale and diffusivity are obtained. The properties of the estimates are discussed in terms of biases and sampling errors, both analytically and using numerical experiments. Optimal sampling for the measurements is studied and an example application to drifter data from the Brazil/Malvinas extension is presented.