The vibrational temperatures of CO and N₂ molecules and their distributions over the radius of the discharge vessel are measured in cryogenically cooled flow-through discharges in He-CO, He-N₂, He-CO-N₂ mixtures. It is shown that in an He-CO-N₂ mixture the vibrational temperatures of CO and N₂ differ significantly by an amount that is in good agreement with theoretical calculations. The vibrational distribution of the CO molecules in a He-CO-N₂ mixture is measured (up to v = 29). It is shown that the populations of the upper vibrational levels are much higher than the Boltzmann values.