Gallium phosphide (GaP) is a promising material for nanophotonics, given its large refractive index and a transparency over most of the visible spectrum. However, since easy phase-matching is not possible with bulk GaP, a comprehensive study of its nonlinear optical properties for harmonic generation, especially when grown as thin films, is still missing. Here, second harmonic generation is studied from epitaxially grown GaP thin films, demonstrating that the absolute conversion efficiencies are comparable to a bulk wafer over the pump wavelength range from 1060 to 1370 nm. Furthermore, the results are compared to nonlinear simulations, and the second order nonlinear susceptibility is extracted, showing a similar dispersion and magnitude to that of the bulk material. Furthermore, the third order nonlinear susceptibility of amorphous GaP thin films is extracted from third harmonic generation to be more than one order of magnitude larger than that of the crystalline material, and generation of up to the fifth harmonic is reported. The results show the potential of crystalline and amorphous thin films for nonlinear optics with nanoantennas and metasurfaces, particularly in the visible to near infrared part of the spectrum.