he possibility of using an active medium to amplify the generated wakefield of an electron beam and employing the amplified wakefield to accelerate a second beam has been recognized recently*. This acceleration scheme is one of several related methods referred to as the Particle Acceleration by Stimulated Emission of Radiation (PASER). However, only the case of an active medium with a single resonant frequency has been analyzed until now. In this paper we present the results of analytical and numerical studies of Cherenkov radiation (CR) in an active medium with two resonant frequencies. We show that this medium can amplify CR even in the case of a purely real refractive index. In contrast to a medium with a single resonant frequency the amplification effect takes place in the absence of metal boundaries but only for sufficiently strong restrictions on the parameters of the medium. The amplification can be effective even for a medium with a relatively small inversion. Examples of CR amplification are given for several active materials. The effect may be useful both for wakefield accelerators and Cherenkov detectors.