The magnetic configuration in the confinement zone of a tokamak admits a magnetic flux-bifurcation for critical values of the edge parameters and given injected power when the initial L-state is so defined as to be associated with a stationary magnetic entropy. Assuming the ITER89-P scaling of the energy confinement time in the L state, it is shown that the power is changing along the bifurcation threshold, for fixed values of the edge parameters, according to the law P=Cn0.77B0.97 (where n is the average density and B is the toroidal magnetic field), where the numerical value of the constant C follows from ITER89-P and is consistent with observations of the L–H transition. It is also shown that the observed independence of the threshold with respect to the current is a consequence of the fact that, at the threshold point, the ratio between the auxiliary power and the Ohmic power PΩ in the confinement region is constant when the current is changing and that the value of PΩ at the threshold is a very slow function of the current.