The main purpose of this paper is the theoretical study and the development of a technique for designing. A low power Reflex-Klystron, in order to construct it in the graduated section laboratories of the Instituto Politecnico Nacional. It is pretended to attain a power of 15-45 m W in frequencies of 8-10 GHz with low acceleration potentials (300-400 V) and electric current of 15-25 m A; the device will be mechanically tuned and will have a fine tuning through the potential of the reflector (150-180 V negative with respect to the resonator). The International System of Units is used in this thesis. (Author).