The electronic surface densities of states of CuNi alloys have been computed in the tight-binding approximation using the moments method. The results are given for (Ool), (110) and (111) surfaces. An electronic model of the surface segregation is then proposed. In this model, the segregation internal energy is deduced from the densities of states. In a first step, the model is analysed within a two-moment theory in which the electronic correlation effects are shown. The theory is in good agreement with existing data on surface segregation in dilute transition metal alloys. Finally, the surface composition of CuNi alloys is computed and is compared with experimental results.