Certain drift waves in tokamaks have the property that they become unstable when thetemperature gradient exceeds a critical value, which increases with increasing density gradient.If instabilities of this type dominate the transport of heat and particles then it is shownthat the particle flux can be a multivalued function of the density gradient. A bifurcation to areduced transport state can then be driven through the density gradient. The conditions for abifurcation to exist are derived. In order for this bifurcation to be observable, trapped particleinstabilities must be suppressed by some other mechanism.