Starting from a mean field calculation for the static capacitance of a MIS-nanostructure with a near back gate [P.N. Racec, E. R. Racec and U. Wulf, Phys. Rev. B 65, 193314, (2002)] we develop an approach to determine the equivalent small-signal circuit. The analyzed system has an open character, taken into account in the Landauer-Büttiker formalism. The Coulomb interaction is treated in Hartree approximation. Consistent with our static calculations we determine the charge-charge correlation function in the random phase approximation to find the ac-admittances. The small-signal circuit consists of a voltage-dependent capacitance and a resistance in series. Beyond a characteristic frequency c ν they become frequency dependent. The characteristic frequency is given by the life time of specific resonance which develops in the system.