For the scattering of acoustic waves by an elastic shell, the acoustical background coefficients are inherent in the scattering coefficients. The background coefficients for elastic empty shells, named the inherent background, can be obtained from the zero frequency limit of the modal accelerance in the scattering coefficients for analogous liquid shells. In this work, the concept of obtaining the inherent background is applied to multilayered elastic cylindrical structures. The inherent background manifests itself in the sound scattering by the liquid structures. The scatteringS-function and the modal accelerance for the liquid system are determined by considering the incoming and outgoing waves. The accelerance of liquid layers is generalized so that the scattering function can be obtained by the recurrence relation for the accelerances of the adjacent liquid layers. From the zero frequency limit of the generalized accelerance of liquid structures, the constant modal accelerance is extracted and the general expression for the inherent background coefficients is obtained. The background coefficients depend on the densities of the layers and ambient fluid medium, the relative thickness of each layer, and the normal mode number. The acoustical background coefficients for solid cylinders, empty shells, fluid-filled shells, and double-layered shells can be obtained by the appropriate limit of the density ratio and the relative thickness of layers in the generalized inherent background coefficients. The usefulness of the proposed background is demonstrated for several examples of layered structures.