In this paper we investigate the appearance of collective oscillations in metal oxide ceramics. This phenomenon is caused by phase fluctuations of order parameters belonging of different energy bands. Band structure calculations for metal oxide ceramics show that on the Fermi surface few energy bands may overlap. This overlapping dramatically changes the properties of superconductors. In such a way, the properties of many-band superconductors differ quantitatively and qualitatively from those of one-band superconductors. For the first time the collective oscillations in usual superconductors have been studied by A. J. Leggett [1]. He pointed out that along with Anderson acoustic mode (ω=0 if k=0) an exciton-like mode caused by the interaction of electron coming from different energy bands appears. Our work is focused on usual two-band superconductors with phonon superconducting mechanism and superconductors with reduced carrier concentration (non-phonon mechanisms of superconductivity). We started from the system for vertex functions according to the model of two – band dirty superconductors [2-4]. We apply this model in the case of reduced concentration when the condition ωDn> μ, (ωDn is the cut – off phononical frequency of the integrals in nth band) takes place, or, generally speaking, when the integration limits are non – symmetrical: (Dcn-Dn)/Dn<<1. Thus, we examine only low impurity concentrations and low frequencies: 1/τnmΔn<<1; ω2/4Δn 2<<1. The last inequality imposes certain restrictions on the values Δ1 and Δ2: the results are correct when Δ1 and Δ2 are the same order values. Further, the equation for frequency of collective oscillations ω and its solution are obtained from the poles appearance condition for the vertex function. The obtained solution ω depends on impurity as well as on the type of superconductor (usual or “exotic”). The main results are the following: • at a low impurity concentration in the case k→0 the collective oscillations aren’t damped out in two – band superconductors • the Bogolyubov – Anderson mode is absent, but an exciton – like mode appears • the frequency ω of this mode is determined by electron – electron interband interaction (which corresponds to the case of native superconductors [1]) and by impurity presence • the frequency ω increases when impurity concentration grows. This fact corresponds to the results obtained by Ginzburg [5] and Maki and Tsuneto [6] related to the appearance of excitons in the superconductors in the case of coupling with momentum different to zero.