The effect of the nonlinear changes of the dispersion characteristics of highfrequency azimuthally symmetric surface waves in a plasma column is investigated theoretically. Both (ω + ω) – ω and (ω – ω) + ω nonlinear interactions of the third order (in relation to the fundamental wave amplitude) are considered here. These two types of interactions influence the wave phase velocity and the collisional damping rate in opposite ways. When ω2Pi/v2 < 1, the contribution of the (ω – ω) – ω interaction is negligible and the (ω + ω) – ω interaction results in an increase of the phase velocity and a decrease of the time damping rate. When ω2pi/v2 > 1, both interactions are involved; the (ω – ω) + ω interaction associated with the ponderomotive force becomes more important, decreasing the phase velocity and increasing the time damping rate (ωpi and v are ion plasma and electron-neutral collision frequencies, respectively).