This work studies the thermal behaviour of a tubular reactor when a reactive fluid is near and at the critical point. A numerical model was developed to simulate the critical behaviour of the fluid in a tubular oxidation reactor during stationary and non-stationary operation. These simulations are validated in steady state by a theoretical analysis and permit to know the thermal behaviour of the reactor. Physical phenomena, which can appear at the critical point, are known for pure water, but their effects in an oxidation reactor containing waste compounds are not studied. Simulated temperatures, velocities and concentrations profiles allow to evaluate the critical reactor behaviour and to identify the conditions of reactor stability. The major conclusion of this study is that the reactor is thermally stable and, in fact, more stable than at classical supercritical conditions. (c) 2005 Elsevier B.V. All rights reserved.