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We complete our study of non-Abelian gauge theories in the framework ofEpstein-Glaser approach to renormalization theory including in the model anarbitrary number of Dirac Fermions. We consider the consistency of the model upto the third order of the perturbation theory. In the second order we obtainpure group theoretical relations expressing a representation property of thenumerical coefficients appearing in the left and right handed components of theinteraction Lagrangian. In the third order of the perturbation theory we obtainthe the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate

The standard model and its generalizations in the Epstein-Glaser approach to renormalization theory: II. The fermion sector and the axial anomaly