The demand for constantly higher competences of employees nowadays is growing permanently. One of the main challenges of implementation of competence management processes is that, as a rule, they are based on the experts' implicit knowledge that practically limits possibilities to transform the already existing knowledge about competences from one organization to another. The paper describes the ontology based competence management process model that is useful for non-formal education service providers in their efforts to use different competence management frameworks together instead of forcing organizations to change their routine competence management processes. The proposed model is based on the previously developed ontology based competence management model which defines more accurately the concept of competence. The competence management process is divided into three main steps - competence identification, competence assessment and competence development. The description of the first step is extended by including the concepts of goal and task to be achieved and performed correspondingly, as well as by adding the concept of creation of competence profile. The conceptual architecture of competence management system based on the prototype with a limited functionality for supporting competence management processes is presented.