The system of two Q-deformed oscillators coupled so that the total Hamiltonian has the su(Q)(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the cross-anharmonicity usually used empirically in describing vibrational spectra of triatomic molecules. The symmetry also imposes a connection between the self-anharmonicity of the Morse oscillators and the cross-anharmonicity strength, which can be removed by replacing the Q-oscillators by deformed anharmonic oscillators. The generalization to n oscillators is straightforward. The applicability of the formalism to highly symmetric polyatomic molecules is discussed.