The aim of the paper is to propose answers to the research question: What are the variables associated with knowledge management, which are conducted by the research groups of higher education institutions -HEI-in Colombia? This problem was identified by analyzing two major tensions. First, between the socially relevant knowledge and knowledge required by the market; and second, between the social research and research oriented by science, technology and innovation. These tensions put the knowledge management, which are conducted by the research groups, at the center of analysis. The methodology used is a case study of a qualitative and descriptive type, for which interviews and analysis of the curriculum vitae of directors and members of research groups were conducted. Review of literature on knowledge management was made, and research done on this topic by HEI. The findings are shown in three groups of variables associated with knowledge management: a) the research structure: planning, resource management, openness to change, leadership, teamwork, initiative, partnership, research training and employment; b) the research process: the problem and research questions, hypotheses, methodology, analysis and interpretation of results, participation in calls, regulation, research platforms and academic production; and c) the innovation process: prospective vision, interaction with the environment, creativity and use of information technologies. The findings indicate that the knowledge management in research groups, should be redirected through institutional policies articulated to the scientific and technological development. Although research groups perform activities resulting from the model of knowledge management (socialization, outsourcing, combination, and internationalization), these are not always practiced in a conscious way; and they also have structural difficulties during the research process, hindering the transfer of knowledge. Taking into account that HEI have integrated management systems that support the research process, it still requires improving the quality of these stages of management. The usefulness of the results leads to rethink policies that guide the processes of institutional research, and redirect knowledge management that is performed from the research groups. This for to move from the structuring of research problems arising from a weak conception of knowledge, to others where sociocultural realities are the benchmark for its formulation. Also aims to consolidate knowledge management from improving academic productivity of research groups, despite the risks of productivism. This is because the productivism is characterized by the proliferation of scientific papers based on the logic of the stacking, but, not of the knowledge creation and its social relevance.. Such practices transformed the publication, which it is a byproduct of the research, in a order of itself.