The nonlinear magneto-optical Kerr-effect has been proposed as an ultrafast spectroscopic probe for the magnetic and electronic properties of ferromagnetic surfaces. The extension of our previous calculation of the linear (first-order) and nonlinear (second-order) magneto-optical susceptibilities by the inclusion of the complete nickel band structure and the dipole transition matrix elements leads to strongly improved agreement between theory and linear magneto-optical experiments. This electronic theory confirms the previous assertion that the nonlinear magneto-optical Kerr-effect should be observable and clearly shows that this effect contains detailed information about the electronic and magnetic surface properties (band structure, exchange interaction, spin-orbit coupling). We discuss possible geometries for experimental and technological applications.