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A power-law, viscoelastic constitutive equation for lithospheric rocks, is considered. The equation is a nonlinear generalization of the Maxwell constitutive equation, in which the viscous deformation depends on the n-th power of deviatoric stress, and describes a medium which is elastic with respect to normal stress, but relaxes deviatoric stress. Power-law exponents equal to 2 and 3, which are most often found in laboratory experiments, are considered. The equation is solved by a perturbative method for a viscoelastic layer subjected to a constant, extensional or compressional, strain rate and yields stress as a function of time, temperature and rock composition. The solution is applied to an ideal extensional boundary zone and shows that the base of the crustal seismogenic layer may be deeper than predicted by a linear rheology.