The influences of interfacial tension and compressibility to the linear viscoelastic properties of nanocomposite and nanoporous materials are considered theoretically. The effective bulk and shear moduli of the systems are calculated within the generalized composite sphere model which takes into account the effect of interfacial tension. It is found that frequency dependence of the effective dynamic shear and bulk moduli of nanocomposites with the compressible elastic matrix and viscous inclusions may be represented in terms of the Zener model comprising of the viscoelastic Kelvin element in series with the elastic spring. The relations of the Zener model parameters with the material characteristics are revealed. The physical interpretation of the frequency behavior of the dynamic shear and bulk moduli against the interfacial tension, component compressibility, viscosity, and inclusion volume fraction is discussed.