In their numerical analysis of convection driven by centrifugal buoyancy in a rotating cylindrical annulus Or and Busse (1987) found that sideband instabilities played an important role. These instabilities correspond to a finite value of the Floquet parameterdand have the tendency to modulate the periodic convection pattern. Since the Galerkin method is not suitable for the study of the convection flow as the sideband instabilities with their small Floquet wavenumberdgrow to finite amplitudes, it was suggested (Busse, 1986) that amplitude equations for the principal modes are investigated to gain at least a qualitative understanding of the problem. The amplitude equations which retain interaction terms up to the cubic order of the amplitude appear to give a fairly accurate description of the symmetric convection columns (Busse and Or, 1986) and of the mean flow solution occurring at higher Rayleigh numbers (Linet al., 1989). The plan was thus conceived to extend the analysis to the case of incommensurate wavenumbers in the azimuthal direction.