The effective gyromagnetic factor of electrons, g e*, has been determined by Zeeman splitting measurements in a large number of Ga As 1− x N x∕ Ga As (x< 0.7%) samples. Upon N incorporation, g e* shows first a sign reversal with respect to that of GaAs, then increases abruptly for a nitrogen concentration of order of 0.04%, and finally displays a nonmonotonic dependence on composition for higher x values. This behavior is well reproduced by a modified k∙ p model taking into account a nonmonotonic loss of Γ character of the conduction band minimum due to multiple crossings between the redshifting conduction band edge and N-cluster states.