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 x 10(13) cm(-2). From the LO-phonon-scattering-limited component of the mobility we obtain for the LO phonon the energy of homega similar to 90 meV and the momentum relaxation time of tau(m) similar to 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 upsilon(d) = 1.0 X 10(7) cm s(-1) at electric fields in excess of E similar to 7.5 kV cm(-1), and at T-L = 300 K it saturates at upsilon(d) similar to 5 x 10(6) cm s(-1), at an electric field of around E similar to 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 mu(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.