Experience has shown that unless special care is exercised in analyzing multiresponse data serious mistakes can be made. In this paper some problems associated with fitting multiresponse models are identified and discussed. In particular, three kinds of dependencies are considered: dependence among the errors, linear dependencies among the expected values of the responses, and linear dependencies in the data. Since ignoring such dependencies can lead to difficulties, a method is described for detecting and handling them. The concepts involved are illustrated with a chemical example.