The theory of the rotation-internal rotation spectra for a rather general class of molecules with an internal rotor of the symmetryC2vis developed in the semi-rigid model approximation. Analytical expressions for the classical and quantum-mechanical hamiltonian are given. It is shown that the energy matrix may be analytically calculated in an appropriate zeroth-order basis composed of rotational and trigonometric wave functions. Symmetry properties of the hamiltonian are given and used extensively in factoring the energy matrix. The irreducible blocks of this matrix are of infinite order. The asymptotic behaviour of the matrix elements far from the diagnoal is shown to beO(ηn) (η< 1;nis the distance from the main diagonal), which is of decisive importance in the numerical diagonalization of such matrices.