The spectra of plasma waves in the electron gas on the surface of a semiconductor nanotube with a superlattice in a parallel magnetic field have been studied using the self-consistent field method. The analytical results for the dispersion relation of the plasmon branch are derived in a tight-binding approximation which takes into account the umklapp effects in the superlattice direction. The long-wave intra-and interband magnetoplasmon frequencies in a degenerate electron gas are calculated both in quasiclassical and in quantum limits. In case of a large number of the filled electron levels, associated with the orbital motion of electrons, the magnetoplasmon frequencies exhibit the oscillations, which are similar to the de Haas-van Alphen oscillations upon variation of nanotube parameters and the Aharonov-Bohm oscillations upon variation of the magnetic flux through the nanotube cross-section.