In this paper, we present a detailed theoretical study on acoustic- and optical-phonon emission by hot electrons in AlxGa1-xAs parabolic quantum wells in parallel magnetic fields. We consider the situation where the phonon generation is detected by phonon emission experiments. The dependence of phonon emission on the magnetic field, excitation power, and phonon emission angle has been studied through calculating the electron energy loss rate in this configuration. The main results obtained from the present theoretical study are the following. (i) In low-, intermediate-, and high-energy excitations, phonon generation is mainly through electron-phonon interaction via piezoelectric, deformation-potential, and polar-optical coupling, respectively. (ii) The strongest acoustic-phonon emission can be observed around a magnetic field at which an electronic subband becomes depopulated, and the strongest LO-phonon emission occurs around a magnetic field where the energy spacing between two subbands equals the LO-phonon energy (electrophonon resonance effect). (iii) Phonon generation in the presence of parallel magnetic fields has a different angular distribution from that at zero and perpendicular magnetic fields.