The topic of process mining has attracted the attention of both researchers and tool vendors in the Business Process Management (BPM) space. The goal of process mining is to discover process models from event logs, i.e., events logged by some information system are used to extract information about activities and their causal relations. Several algorithms have been proposed for process mining. Many of these algorithms cannot deal with concurrency. Other typical problems are the presence of duplicate activities, hidden activities, non-free-choice constructs, etc. In addition, real-life logs contain noise (e.g., exceptions or incorrectly logged events) and are typically incomplete (i.e., the event logs contain only a fragment of all possible behaviors). To tackle these problems we propose a completely new approach based on genetic algorithms. As can be expected, a genetic approach is able to deal with noise and incompleteness. However, it is not easy to represent processes properly in a genetic setting. In this paper, we show a genetic process mining approach using the so-called causal matrix as a representation for individuals. We elaborate on the relation between Petri nets and this representation and show that genetic algorithms can be used to discover Petri net models from event logs. Keywords: Process Mining, Petri Nets, Genetic Algorithms, Process Discovery, Business Process Intelligence, Business Activity Monitoring.