The transient flow behaviour of groundwater in an aquifer-aquitard system with viscoelastic properties is studied. On the basis of previous work (Hantush, Neuman, Brutsaert, Corapcioglu), new partial-differential integral equations are assembled. The well-known equations (Hantush, Brutsaert) are special cases of these equations, which describe the flow of slightly compressible groundwater in aquifer-aquitard layers with viscoelastic properties. Analytical solutions of the coupled partial differential-integral equations are obtained by Laplace transform. The viscoelastic properties enhance the heterogeneities of an elastic aquifer system with delay and feed. Numerical inversion of the Laplace transformed drawdown is in good agreement with the analytical solutions obtained.