We report the experimental studies of hot-electron energy and momentum relaxation in the steady state in GaN/AlGaN HEMT structures with a high two-dimensional electron density of n = 1.5×10¹³ cm^-2. From the LO-phonon-scattering-limited component of the mobility we obtain for the LO phonon the energy of ω~90 meV and the momentum relaxation time of τ_m~4 fs. Drift velocity versus electric field characteristics obtained from the pulsed I-V measurements show that, at T_L = 77 K, the drift velocity saturates at v_d = 1.0×10⁷ cm s^-1 at electric fields in excess of E~7.5 kV cm^-1, and at T_L = 300 K it saturates at v_d~5×10⁶ cm s^-1, at an electric field of around E~10 kV cm^-1. Electron temperature as a function of applied electric field is obtained by comparing the measured electric field dependence of the mobility µ_E at a fixed lattice temperature, with the lattice temperature dependence of the mobility at a fixed low electric field. The electron energy loss rate is then determined from the electron temperature dependence of the power loss using the power balance equations. The effect of hot-phonon production on the observed momentum and energy relaxation of hot electrons is discussed within the framework of a theoretical model, which was originally developed for III-V material systems and has been adapted for a two-dimensional electron gas in GaN, and in which phonon drift is neglected.