Process Mining is a novel alternative to analyze the real processes, from extraction of knowledge of the event logs available in the information systems. The discovery is one type of process mining that allows obtaining process models, which can be observed visually eventualities in the processes modeled. Inductive Visual Miner is a plugin of ProM tool that supports the discovery and can generate animated process models inspired in a Business Process Modeling Notation. Actually, the knowledge needed to model hospital processes is acquired from empirical methods of researchers in the health institution. Hospital Information Systems possess an event log of processes activities, and it is not being exploited to detect eventualities in hospital processes. This research focused on the development of an Inductive Visual Miner customization, for the detection of eventualities in hospital processes. To develop the solution was used Java 1.6 as programming language, JBoss 4.2 as the application Server and Eclipse 3.4 as Integrated Development Environment. Java Enterprise Edition 5.0 platform was used during the whole process. The investigation allows to generate models of processes where can be observed eventualities of hospital processes.