The method of the effective operators is applied to the global treatment of the vibrational–rotational spectra of the linear CO2 and N2O triatomic molecules. The problems in calculations of the line centers and the line intensities are considered. For these purposes the models of the reduced effective Hamiltonians and the corresponding effective dipole moment operators are proposed. The parameters of these operators are found by the least–square fittings of the experimental line centers and line intensities. Good extrapolation properties of the proposed models are demonstrated.