In our companion article (Color Res Appl 2013) we compared the use of Basic Color Terms (BCTs) by normal trichromats, protanopes, and deuteranopes in a mapping (which colors are instances of X?) and best exemplar (which is the best X?) tasks. In this article, we describe and compare two alternative models of the mechanisms underlying the use of Basic Color Terms (BCTs) by red-green dichromats and we focus on how well they fit the empirical data described in the companion article. Model A assumes that BCT use is based on the activity of the yellow-blue and lightness channels, whereas Model B also assumes that there is some degree of input from the red-green channel. Model B was more accurate than Model A in predicting: (1) The frequency of use of BCTs. (2) The distribution of correct responses for many BCTs in both tasks. (3) The distribution of correct responses and kind of errors for many BCTs. (4) The locations of the centroids for both tasks. We conclude that activity in a "residual" red-green channel influences the use of BCTs by R-G dichromats, as well as the activity of the yellow-blue and lightness channels. The asymmetry of errors for some pairs of BCTs and the differences between primary and derived BCTs are also discussed. This article, in combination with its complementary one (Color Res Appl 2013), provides a comprehensive and detailed overview of how R-G dichromats use BCTs to categorize surface colors and can integrate and explain some of the results and conclusions obtained in earlier research. (C) 2013 Wiley Periodicals, Inc.