Several theoretical analyses of the process of magnetization reversal in thin films by coherent rotation of the magnetization vector have been published. However, these analyses suffer from the use of questionable assumptions and from a lack of generality. This paper presents results obtained by employing an electronic digital computer to solve differential equations of greater accuracy and generality than those previously used. These results show how the optimum damping factor (which, as defined herein, differs slightly from the critical damping factor), the peak output voltage, and the reversal time vary with the magnitude and direction of a field applied to a thin ferromagnetic film with uniaxial anisotropy. The results for a particular direction of applied field show that the optimum damping factor and the peak voltage increase and the reversal time decreases with increasing magnitude of the field; and that a plot of reciprocal reversal timeversusfield magnitude is a parabola if the damping factor is always equal to its optimum value, but a hyperbola if the damping factor is a constant.