This paper presents a novel methodology for multiple failure modes prognostics in rotating machinery. The methodology merges a machine learning and pattern recognition approach, called logical analysis of data (LAD), with non-parametric cumulative incidence functions (CIFs). It considers the condition monitoring data collected from a system that experiences several competing failure modes over its life span. LAD is used as a non-statistical classification technique to detect the actual state of the system, based on the condition monitoring data. The CIF provides an estimate for the marginal probability of each failure mode in the presence of the other competing failure modes. Accordingly, the assumption of independence between the failure modes, which is essential in many prognostic methods, is irrelevant in this paper. The proposed methodology is validated using vibration data collected from bearing test rigs. The obtained results are compared to those of two common machine learning prediction techniques: the artificial neural network and support vector regression. The comparison shows that the proposed methodology has a stable performance and can predict the remaining useful life of an individual system accurately, in the presence of multiple failure modes.