This letter proposes a nonlinear hybrid model method to assess a bearing component's health for long-term prediction of the remaining useful life (RUL) before a breakdown occurs. This model uses neural training of a recursive extreme learning machine (RELM) core integrated with a Monte Carlo-based framework. Estimation of the model's parameters, along with the system states, is used to construct an updated model that is utilized for prediction. Practical experiments using the public benchmark dataset indicate that the RELM method demonstrates superior effectiveness for RUL estimation, as measured by the (α-λ) metric and the cumulative relative accuracy.