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Dynamic characteristics of a quasi-low-dimensional semi-bounded anisotropic lattice with a local defect in a subsurface region are studied. Quasi-one-dimensional and quasi-two-dimensional systems are considered. The effect of a distortion at a surface is also taken into account. Differences between 1D or 2D system and quasi-low-dimensional 3D systems are investigated. Peculiarities in the density of states of volume and surface excitations and thresholds of surface and local excitations are analyzed.