This chapter presents a holistic method to addresses the issue of health monitoring of system parameters in Bond Graph (BG). The advantages of BGs are integrated with Bayesian estimation techniques for efficient diagnostics and prog-nostics of faults. In particular, BG in Linear fractional transformations (LFT) are used for modelling the global uncertain system and sequential Monte Carlo method based Particle filters (PF) are used for estimation of state of health (SOH) and subsequent prediction of the remaining useful life (RUL). In this work, the method is described with respect to a single system parameter which is chosen as prognos-tic candidate. The prognostic candidate undergoes progressive degradation and its degradation model is assumed to be known a priori. The system operates in control feedback loop. The detection of degradation initiation is achieved using BG LFT based robust fault detection technique. The latter forms an efficient diagnostic module. PFs are exploited for efficient Bayesian inference of SOH of the prog-nostic candidate. Moreover, prognostics is achieved by assessment of RUL in probabilistic domain. The issue of prognostics is formulated as joint state-parameter estimation problem, a hybrid prognostic approach, wherein the fault model is constructed by considering the statistical degradation model of the prog-nostic candidate. The observation equation is constructed from nominal part of the BG-LFT derived Analytical Redundancy Relations (ARR). Various uncertainties which arise because of noise on ARR based measurements, degradation process, environmental conditions etc. are effectively managed by PF. This allows the production of effective predictions of the RUL of the prognostic candidate with suitable confidence bounds. The method is applied over a mechatronic system in real time and performance is assessed using suitable metrics.