The evolution of computing technology and wireless networks has contributed to the miniaturization of mobile devices and their increase in power, providing services anywhere and anytime. In this scenario, applications have considered the user's contexts to make decisions (Context Awareness). Context-aware applications have enabled new opportunities in different areas, for example, education, games and entertainment, commerce, and competence management. In this article, we present MultCComp, a multi-temporal context-aware system for competences management. The main system contribution is to take advantage of the workers' present and past contexts to help them to develop their competences. We define as multi-temporal context awareness the joint use of workers' present and past contexts to assist them in the development of their competences. We developed a prototype and conducted two experiments with it in an evaluation environment. The first experiment aimed to demonstrate the system functionalities. It consisted of two evaluation scenarios that were followed by two users. The second experiment focused on evaluating the acceptance of the system. It comprised a scenario that was followed by 21 users, who filled out a questionnaire at the end of the test.