This paper shows the results of the proposal and application of knowledge management (KM) model based on third-order cybernetics in the productive chain tanned leather. A statistical relationship between the components of the cycles of KM was established through the use of correlational statistical models, obtaining of the multivalent relationships between the components identified in feedback loops KM observed in enterprises and their divergence from the model conceptual, originating as a result diagnostic of current practices in the production chain KM tanned leather in Bogotá Also, it established a starting point for generating innovation strategies and development of the productive sector of leather, to detect some deficiencies in the feedback loops of the KM, which were extracted from the summary of regression equations on flows of information and knowledge in productive factors considered in the production chain of tanning leather.