We consider adaptive regulation of the temperature for exothermic chemical reactors. These reactors may exhibit multiple steady states, and the relevant operating point could be an unstable open-loop equilibrium. The adaptive controller combines the so called À-tracking approach with a feedback which obeys a saturation; it is simple in its design, does not invoke an observer, and can cope with measurement noise. Tracking is achieved up to any pre-specified accuracy, the choice of which is left to the designer. The class of exothermic chemical reactors to which the controller is applicable is considerably larger than the classes to which robust (non-adaptive) global stabilisers, previously studied in the literature, can be applied. The adaptive control strategy does not require any knowledge of the systems parameters and does not invoke an internal model. It is only assumed that the reference temperature to be tracked is feasible. The problem of temperature tracking is solved both locally, i.e. the temperature must lie in a bounded interval, and globally.