The fundamental limitations for the efficiency of cathodoluminescence of phosphors attract interest owing to the development of highly efficient field emission light sources. The most general limitations imposed on the luminescent radiation by thermodynamics were analyzed in [1, 2]. Since the entropy of the electron beam is rather low, the efficiency of cathodoluminescence could be very high, close to 100% [2]. However, in practice the energy yield of cathodoluminophores does not exceed 25% [3-5]. The host matrix (its crystal lattice exhibits semiconductor properties) absorbs the energy of fast electrons and transforms it into the energy of electron-hole pairs, which subsequently thermalize and excite the luminescence centers when captured by them. The main losses of the initial energy (more than 60 %) occur during the thermalization stage. The subsequent losses occur, which can be in principle reduced or eliminated: the losses due to the nonradiative recombination on the lattice defects and so called Stokes losses, since the energy of the photon emitted by the luminescence center is always less than the forbidden gap of the host matrix (usually by no less than 15%). Thermalization losses and Stokes losses (after [3]). The average energy of creation of electron-hole pair is β·Eg, where Eg is the forbidden gap of the host matrix, and β is a coefficient, which characterizes the thermalization losses. Starting from the experimental data, this coefficient is usually taken as β ~ 3 (see, for example, [6]). As Yu.M. Popov has shown [3], this is associated with the semiconductor band structure, and β ~ 3 for direct-gap materials where the effective masses of electrons and holes are approximately equal (this is valid for the large majority of substances used as cathodoluminophore hosts); from this follows that the efficiency cannot exceed 33%. However, it was shown in [7] that for alkali halide compounds β can be less than 3 owing to the peculiar features of their energy band structure, and the luminescence efficiency can reach 35 - 70%. Therefore, one can suggest that the ways exist to considerably increase the efficiency of cathodoluminophores.