The constrained linear inversion technique and the optimal estimation method are applied to joint retrievals of atmospheric constituent profiles from vertical sounding spectra in the millimeterwave range. The algorithms are illustrated on dual profile retrievals of ozone (O₃) and chlorine monoxide (ClO) from synthesized spectra and on dual profile retrievals of ozone and chlorine monoxide, of ozone and nitrous oxide (N₂O), and of ozone and nitric acid (HNO₃), respectively, from measurements performed with the ground-based millimeterwave radiometer MIRA II during February and March 1996 at Kiruna. Reconstructed profiles are compared to observations performed by other groups. The joint retrieval concept proves to be a useful tool that provides valuable information about the altitude distribution of atmospheric constituents.