Several magnetic and optical processes contribute to the magneto-optical response of nickel thin films after excitation by a femtosecond laser pulse. We achieved a first complete identification by explicitly measuring the time-resolved Kerr ellipticity and rotation, as well as its temperature and magnetic field dependence in epitaxially grown (111) and (001) oriented Cu/Ni/Cu wedges. The first hundreds of femtoseconds the response is dominated by state filling effects. The true demagnetization takes approximately 0.5-1 ps. At the longer (sub-ns) time scales the spins are found to precess in their anisotropy field. Simple and transparent models are introduced to substantiate our interpretation.