Spin-flip Raman scattering spectroscopy has been applied to the study of the wide band-gap semiconductor material Zn1-xCdxSe in order to determine for the first time the dependence on the composition, x, of the gyromagnetic ratio of electrons in the Gamma(6) conduction band. The experimental values for the Zn1-xCdxSe, Zn1-xMgxSe and ZnSxSe1-x alloy systems are discussed in terms of the k.p perturbation theory for the band structure near the direct band gap and it is found that the observed dependence on composition can be reproduced well only when the five-band level of approximation is used together with the addition of a third-order perturbation term. Simple interpolation schemes have been used to estimate the band structures between the binary end-members of each alloy, taking into account the bowing of the fundamental band gay and making reasonable assumptions about the behaviour of the spin-orbit coupling parameter.