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The theory describing the relaxation of an incompressible, layered Maxwell half-space is developed. The approach is based on the analytic solution of the associated elastic model and the subsequent application of the correspondence principle. The viscoelastic theory follows normal-mode theory, which allows the independent and exact determination of the relaxation-time and amplitude spectra for each mode of relaxation. The solution is tested by calculating the response of several models in the wavenumber and spatial domains. The examples are selected with regard to postglacial adjustment in Fennoscandia and analyse effects caused by (a) varying lithospheric thickness, (b) adding an asthenosphere, (c) increasing lower-mantle viscosity, (d) permitting relaxation of the lower lithosphere or (e) introducing density contrasts at 400-km and 670-km depths.
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