In the context of intensive discussion regarding the effectiveness of internal studies' quality management systems implemented by universities and the potential of generic quality management models developed outside of higher education to contribute tangibly, this paper aims to perform the analysis and comparison of specific and generic quality management models applied by universities within the European Higher Education Area and to discover whether generic quality management models are relevant for European universities of today and how can they be applied. Methods of document analysis, modelling, classification and comparative analysis have been employed for the research. Results reveal that some elements of generic quality management models can compensate weak points of specific ones. Thus, the approach for European universities of how to integrate these different models is proposed in the paper.