The method for revealing of the weak oscillations in the frequency dependence of the electroconductivity of the metallic nanoparticles is proposed. The calculations are realized using the kinetic equations method which allows accounting effectively the electron scattering on the inner surface of the particle. The frequency dependence of the ratio of kinetic $\sigma_{\textrm{kinet}}$($\omega$) and classic $\sigma_{\textrm{clas}}$($\omega$) electroconductivities for spherical metal nanoparticles of an arbitrary sizes is investigated. The amplification of the weak oscillations of the kinetic electroconductivity with frequency is established in metal nanoparticle for ratio of $\sigma_{\textrm{kinet}}$($\omega$)/$\sigma_{\textrm{clas}}$($\omega$). It has the greater amplitude than smaller radius of metal nanoparticle is. The Ag nanoparticle is used as an example for illustration.