In this work a theoretical and experimental study was carried out to observe the instability in a reactor. The first instability concerns the multiplication of stationary states. This instability was observed by simulation and experiment. The second instability concerning the observation of a sustained periodic instability called limit cycle, which appears as a periodical variation maintained by the state of the system. This second instability was observed by simulation, but could not be obtained in the experiments (exothermic reaction between Na2S2O3 and H2O2), also not in a new reactor with improved cooling system. This can be explained by the complex conditions to obtain the limit cycle as well as the sensitivity of this zone to the operating conditions and probably due to the high inertia of the coil.