Propagating in the nonferromagnetic electron gas on the cylindrical nanotube's surface spin waves in longitudinal magnetic field are considered. The spectrum of electrons in the Hartree–Fock approximation was applied. The dynamic spin susceptibility of a degenerate electron gas was derived using the random phase approximation. The spectra of intra-subband and inter-subband magnons were calculated in quasiclassical and quantum limits. The quantity of spin waves spectrum branches depends on the amount of filled subbands. In case the filled subband numbers are large, the wave's frequencies undergo oscillations of de Haas–van Alphen and Aharonov–Bohm types with the electron density and the magnetic induction changes.