A hybrid deep learning and machine learning approach for both failure mode classification and time-to-failure prediction is proposed in this dissertation, with a focus on a multi-mode failure regime where the state of health of components can vary. To validate the potential performance of the proposed approach, a vehicle's leaking hydraulic suspension system is simulated via a quarter car model as a proof of concept. Next, the quarter car model is expanded to include a model of a failing engine mount. The dynamic data from these models is employed to train a NARX net with the health condition and degradation rate as an output. The predictive capabilities of the NARX given this data is significant, validating the proposed approach. To develop the hybrid approach, a four-cylinder diesel engine with EGR and VGT is simulated over a prescribed operational range for four failure types. A multi-label CNN model is utilized to classify which multi-mode failure modes are occurring while hiding health condition information. The approach resulted in significant performance in classifying the failure modes. This data is then employed in regression models to determine the health condition of various components. It was determined that utilizing this data and previous state information with ensemble tree methods and neural networks results in predictive accuracy with less than 3% normalized root mean square error. Finally, a NARX net approach for determining the degradation rate and time-to-failure of a component utilizing this health condition information is verified. A discussion on how these approaches can be combined to create a hybrid predictive model that determines the engine's probable failing time is presented. Based on the results from each stage of the hybrid model, it is expected that this approach can provide significant predictive performance in monitoring the health of a diesel engine as well as any similar system with comparable failure modes.