Nonlinear periodic waves in a stratified fluid stationary with respect to a rotating cylindrical system are studied. The case to be considered is that of an incompressible, inviscid fluid with free surface rotating about a rigid circular cylinder and pulled toward the axis of the cylinder by a constant body force. Critical angular speeds, near which such periodic waves are possible, are determined by the eigenvalues of an eigenvalue problem, and the equation governing the wave profiles is then obtained by a compatibility condition. With slight modification, the method developed is applied to other cases of interest.