The flow of high temperature nitrogen gas through a converging-diverging conical test nozzle is simulated under conditions of thermodynamical nonequilibrium. The flow is simulated using the Navier-Stokes equations that have been modified to include the effects of intermolecular forces and vibrational nonequilibrium. In particular, two energy equations are used. One energy equation accounts for energy effects due to translational and rotational degrees of freedom. The other energy equation models effects due to the vibrational degree of freedom. These energy equations are coupled using an improved relaxation time over the temperature range of the flow. The computational fluid dynamics algorithm of Steger-Warming flux vector splitting method was employed to solve the resulting equations. The equations were also solved using the implicit MacCormack method as a check of the computations. Both of these methods produced consistent numerical results. Our simulation showed that a uniform flow was produced outside the boundary layer and that nonequilibrium exists in both the converging and diverging nozzle sections. The boundary layer exhibited a marked increase in the translational-rotational temperature. The vibrational temperature, away from the boundary layer, remains essentially frozen downstream of the nozzle and along the center line.