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The damping of longitudinal waves in colloidal crystals, considered in the primitive plasmalike model ͑counterions and macroions in liquid͒, is investigated in the framework of viscoelastic theory in continuous approximation. The transition from the discrete lattice to the continuous approximation for longitudinal waves is possible, because the wavelength is much larger than the lattice parameter. The dispersion relations, numerical and analytical results for the bulk and surface modes are found for the infinite, semifinite, and finite size crystals. On this basis the experimental results obtained earlier by Hoppenbrouwers and van de Water ͑unpub-lished͒ in finite size crystals are compared with our theoretical results. ͓S1063-651X͑96͒08412-7͔

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Real dusty crystals are inhomogeneous due to the presence of external forces.