We study the magnetotransport properties of high-mobility holes in monolayer and bilayer WSe_{2}, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states in high magnetic fields. In both mono- and bilayer WSe_{2}, the SdH oscillations and the quantum Hall states occur predominantly at even filling factors, evincing a twofold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe_{2} reveals the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of the SdH oscillations we determine a hole effective mass of 0.45m_{0} for both mono- and bilayer WSe_{2}.