Processes of the supersonic flow of the vibrationally nonequilibrium gas in expanding nozzles are investigated. Processes of the vibrational relaxation in a gas of anharmonic oscillators are separated into stages with the different nonequilibrium degree. The quasi-stationary distribution functions are written for each of these stages. The gas dynamic description of corresponding flows is given at the level of minimum number of macroparameters. The molecular nitrogen flow in the supersonic conic nozzle is investigated on the basis of the proposed model.