In this paper adaptive predictors structured in cascade form are used to analyse superimposed exponential signals with time-varying parameters. On-line optimisation of the filters parameters is achieved using gradient descent techniques focused on the direct estimation of instantaneous information-bearing parameters (damping and frequency). Examples of the performance of the algorithm are given for real-valued multi-component synthetic signals with different schemes of frequency modulation in clean and noisy environments. The performance of the algorithm is also evaluated in the task of tracking the formants of a voiced segment of speech. (C) 2001 Elsevier Science BY. All rights reserved.