Inverse problems of the remote sensing of the atmosphere are formulated for the general case of an optically thick atmosphere under non-local thermodynamic equilibrium condition for the space-borne spectral measurements of the limb i.r. radiation. A feasibility study of the retrieval of the vertical profiles of different atmospheric parameters [vibrational (T_ν) and kinetic (T_kin) temperatures, concentration of the absorbing gases, pressure] has been carried out by means of the error matrix calculations (optimal estimation method) for different spectral intervals of measurements (15 μm CO₂ bands, 9.6 μm O₃ bands and 10 μm CO₂ laser bands), different spectral resolutions Δν and wide range of noise equivalent radiance (NER) values. It has been shown that limb radiation spectral measurements, for example, in 15 μm CO₂ band (Δν = 1 cm^-1, NER corresponding to MIPAS interferometer) enable the retrieval of T_v for CO₂ states 01¹0, 02⁰0, 02²0, 10⁰0 with an error less than half of the a priori uncertainty up to 112.5, 100, 102.5 and 100 km, respectively. Limb radiation measurements in the 9.6 μm O₃ band make it possible to retrieve, with an accuracy about 10-30% of the a priori uncertainty, the vertical profile of the ozone concentration up to 65-90 km depending on the NER value, Δν and atmospheric model. The lower limit retrieval errors for O₃ vibrational temperatures strongly depend on NER, Δν and the vibrational state under consideration, especially in the layers higher than 65 km. More than 50% decrease of a priori uncertainties (an error less than 25 K) is observed for the states of O₃ molecule 001, 100, 011, 003, 012 up to 102, 94, 93, 92, 90 km, respectively (for Δν = 2.5 cm^-1 and NER 10 times lower than one for MIPAS). Limb radiation measurements yield a considerable decrease (50-80%) of the a priori uncertainty of the pressure profile in the height range 30-60 km. If T_kin is considered as an independent unknown variable, the considerable amount of information on T_kin (up to 90-95 km) can be obtained only when NER is low, which is characteristic, for example, for CLAES instrument. Different ideas concerning the improvement of the retrieval accuracy are discussed.