This paper presents a generic data-driven failure prognosis method based on adaptive state space models for engineering systems, which integrates adaptive model recognition with a dynamic system model for remaining useful life prediction. The developed approach employs a statistical learning framework for adaptively learning of time-series degradation performance, and then a Bayesian technique for self-updating of data-driven models to adapt the operational or environmental changes. With the developed approach, the prognosis technique can eliminate the dependence to system specific models and be adaptive to system performance changes due to degradation or variation of system operational conditions, thereby yielding accurate remaining useful life predictions. The developed methodology is demonstrated by an engineering case study.