A detailed study of the quasi-1D magnetoplasmon frequencies (Ψp) in a single tubule is given by the random phase approximation. The excitations are specified by the linear momentum (q), the angular momentum (L), and the magnetic flux (Φ) through the tubule. The & dependent Ψp, exhibits an oscillatory feature including many cusps. The spin-B interaction is important, because it doubles the number of cusps and destroys the periodicity (period Φ0 = hc/e) of the &dependent frequency. The approximate Ψp from the large-w expansion is useful in understanding the strong Φ- and q-dependence. The effects of the local-field corrections on the magnitude of Ψp (q, L, Φ) are obvious. The structure near the cusps is examined, and is found to be related to the important band parameters (e.g., effective mass). The intertubule Coulomb interaction is included in studying the magnetoplasmons of the coaxial tubules. The similar features are obtained for a two-tubule system, and they could be generalized to any n-tubule system.