The effect of longitudinal plasma flow on transverse oscillations in the thin magnetic tubes with elliptical cross-sections is examined. The backward propagating waves of the $M$ -kink mode (polarized along the major axis) and $m$ -kink mode (polarized along the minor axis) are found to reverse their propagation direction at certain flow thresholds. The critical flow for the $M$ -kink mode is lower than in a circular tube and is close to the internal Alfvén speed. This result is of particular interest within the concept of existence of negative energy waves in solar waveguides. Both modes are subjected to the Kelvin–Helmholtz (KH) instability, and the $M$ -mode is more stable than the $m$ -mode. Magnetic tubes with significant ellipticity are more resistant to the KH instability than circular tubes. In the quasi-standing wave regime, the frequencies of both modes decrease and the frequency ratio $\omega _{m}/\omega _{M}$ increases with faster flows. The obtained results are used to interpret the observed transverse oscillations of the solar limb spicules and their helical motions in terms of the $M$ - and $m$ -kink modes.
