The onset of convection in binary fluid mixtures in a rotating vertical cylinder is considered. Parameter values and boundary conditions relevant to experiments on3He–4He mixtures with negative separation ratio are used. The eigenfunctions take the form of rigidly precessing spirals. The azimuthal wavenumber of the first unstable mode as the Rayleigh number increases is calculated as a function of the rotation rate and the separation ratio, as are the critical Rayleigh numbers and precession frequencies. Depending on the parameters the spirals may take the form of spatially extended body modes which fill the container, or of wall modes confined to its boundary. The former typically precess in the retrograde direction, while the latter are prograde. Under appropriate circumstances the binary system with a negative separation ratio becomes unstable for lower Rayleigh numbers than a pure fluid. This property of the system is enhanced by the wall modes. ©1995 American Institute of Physics.