The oscillator strengths for optical transitions involving the lowest pair of the single-electron energy subbands are evaluated within the dipole approximation as functions of the axial applied magnetic ΓΏeld for the di erent forms of the conΓΏning potential. The radiation ΓΏeld with clear-cut selection rules is that of circularly polarized light along the axis of the cylinder. The allowed transitions are only those between the subbands whose azimuthal quantum numbers di er by unity. The applied magnetic ΓΏeld lifts the degeneracy of the doubly degenerate non-zero azimuthal quantum number states and thereby leads to a very di erent behaviour of the oscillator strengths for the (0 β 1) and the (0 β -1) transitions, which are otherwise the same in the absence of an applied magnetic ΓΏeld. The main prediction here is the enhancement of the strength of the optical transitions for which the energy separations of the relevant subbands open up as the magnetic ΓΏeld is increased. Some approximate wavefunctions are employed to obtain analytical results for the oscillator strengths for optical transitions involving the three lowest subbands. There is complete agreement between the analytical and the exact numerical results even for a large radius of the cylinder and for high magnetic ΓΏelds.