A large class of stationary signals, containing speech signals, but not restricted to them, can be represented by time-varying models, the coefficients of which are finite linear combinations of known time functions. Such models have been found useful for speech recognition and speech synthesis, but they suffer in this last application from a lack of stability. A time-varying area-ratio (AR) model, into which the time-dependency is coded through log-area ratios to ensure stability is described. Two algorithms for the estimation of these time-varying log area ratios are proposed; the first one is an approximation using a lattice filter, while the second one minimizes a least-squares criterion. The evaluation of their performance is obtained by a set of simulations. An example of speech signal modeled with these time-varying log area ratios shows the usefulness of this approach for speech synthesis and recognition.<>