Using different nucleation layers, we have grown cubic and hexagonal GaN epilayers on (001)-oriented GaAs substrates by radio-frequency plasma-assisted molecular beam epitaxy. First- and second-order Raman spectra are taken from these epilayers in back-scattering configurations at room temperature. For the first-order Raman spectra, transverse-optical (TO) phonons and longitudinal-optical (LO) phonons of cubic GaN are found to be at 533 and 739 cm(-1), as well as the E-2 and A(1)(LO) frequency of hexagonal GaN are found to be at 568 and 733 cm(-1), and the polarized spectra are in good agreement with Raman selection rules for cubic and hexagonal GaN, respectively. These results confirm the single crystalline nature of the samples. As for the second-order Raman spectra, the bands show a continuum, at about twice the energy of the LO phonon of cubic GaN and A(1)(LO) phonon of hexagonal GaN, which are nearly 10 times weaker than the first-order scattering. Two-phonon spectra are dominated by contributions due to longitudinal optical phonons.