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The theory of the rotation-internal rotation spectra for a rather general class of molecules with an internal rotor of the symmetry C2v is 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 be O(ηn) (η < 1; n is the distance from the main diagonal), which is of decisive importance in the numerical diagonalization of such matrices.A few numerical examples for a model are given in order to demonstrate the high precision achievable in the infinite matrix diagonalization. Furthermore the internal rotation problem (J = 0 states) is discussed, including the application to actual barrier determination from far infra-red spectra or microwave spectra as well as a comparison with the symmetric internal rotor case. Finally selection rules for electric dipole transitions and analytical expressions for the line strengths are given. It is shown that the theory can be developed to the same degree of explicitness as in the case of the rigid asymmetric rotor.