In this manuscript, contributions to the development of methods for on-line model-based prognosis are presented. Model-based prognosis aims at predicting the time before the monitored system reaches a failure state, using a physics-based model of the degradation. This time before failure is called the remaining useful life (RUL) of the system.Model-based prognosis is divided in two main steps: (i) current degradation state estimation and (ii) future degradation state prediction to predict the RUL. The first step, which consists in estimating the current degradation state using the measurements, is performed with filtering techniques. The second step is realized with uncertainty propagation methods. The main challenge in prognosis is to take the different uncertainty sources into account in order to obtain a measure of the RUL uncertainty. There are mainly model uncertainty, measurement uncertainty and future uncertainty (loading, operating conditions, etc.). Thus, probabilistic and set-membership methods for model-based prognosis are investigated in this thesis to tackle these uncertainties.The ability of an extended Kalman filter and a particle filter to perform RUL prognosis in presence of model and measurement uncertainty is first studied using a nonlinear fatigue crack growth model based on the Paris' law and synthetic data. Then, the particle filter combined to a detection algorithm (cumulative sum algorithm) is applied to a more realistic case study, which is fatigue crack growth prognosis in composite materials under variable amplitude loading. This time, model uncertainty, measurement uncertainty and future loading uncertainty are taken into account, and real data are used. Then, two set-membership model-based prognosis methods based on constraint satisfaction and unknown input interval observer for linear discete-time systems are presented. Finally, an extension of a reliability analysis method to model-based prognosis, namely the inverse first-order reliability method (Inverse FORM), is presented.In each case study, performance evaluation metrics (accuracy, precision and timeliness) are calculated in order to make a comparison between the proposed methods.