Intensity profiles of infrared spectral lines of stratospheric constituents can be fully resolved with a heterodyne spectrometer of sufficiently high resolution (~5MHz or 0.000167 cm1 at 10&mgr;). The constituents' vertical distributions can then be evaluated accurately by analytic inversion of the measured line profiles. Estimates of the detection sensitivity of a heterodyne receiver are given in terms of minimum detectable volume mixing ratios of stratospheric constituents, indicating a large number of minor constituents which can be studied. Stratospheric spectral line shapes and the resolution required to measure them are discussed in light of calculated synthetic line profiles for some stratospheric molecules in a model atmosphere. The inversion technique for evaluation of gas concentration profiles is briefly described, and applications to synthetic lines of O3, CO2, CH4, N2O are given. Some recent heterodyne measurements of CO2 and O3 absorption lines are analytically inverted, and the vertical distributions of the two gases are determined.