Inverse problem of thermal radiation transfer accounting for non-LTE effects has been considered for limb geometry in the spectral region covering 10.4μm, 15μm CO₂ and 9.6μm O₃ bands. Limb radiance has been calculated line-by-line on the basis of the non-LTE model describing day-time non-equilibrium populations of the vibrational states of CO₂ and O₃ molecules which correspond to the bands under consideration. The inverse problem for the satellite limb radiance high resolution measurements in the spectral interval 540-1150 cm^-1 has been posed with respect to the simultaneous retrieval of the vertical profiles of pressure, kinetic temperature, number density of main absorbers, and vibrational temperatures of the states mentioned above. For the estimation of the retrieval accuracy the optimal estimation method has been applied, and the calculations of error matrices have been performed. The influence of the spectral resolution of measurements on the retrieval accuracy has been investigated. The conclusion has been done on the applicability of measurements to be performed in future by instruments similar to MIPAS to the investigations of non-LTE effects in the middle atmosphere.