The effective gyromagnetic factor of electrons, ge*, has been determined by Zeeman splitting measurements in a large number of Ga As1-x Nx GaAs (x<0.7%) samples. Upon N incorporation, ge* 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 kp 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.