It has been known for many years that in a circular counterflow pipe there exist two different states of turbulence of helium II: the T-1 state, which appears at low values of heat flux, and the T-2 state, which appears suddenly at higher heat flux and is characterized by a much higher density of quantized vortex lines. Until now the nature of the two turbulent states has been a mystery. To understand this problem we have addressed the issue of the velocity profile of the normal fluid and its stability. The computed critical heat flux of the transition from the T-1 state to the T-2 state is found to be in good agreement with the observations. The result indicates that in the T-1 state the superfluid is turbulent but the normal fluid is still laminar. The T-1 to T-2 transition corresponds to the onset of normal fluid turbulence.