A theory of linear viscoelasticity is developed for dilute polymer solutions in viscoelastic solvents. The non-Markovian dynamics of a macromolecule with hydrodynamic interaction is analyzed on the basis of a generalized Langevin equation with relaxed friction. The relaxation spectrum (relaxation times and elastic moduli) of the solutions is calculated for a simple viscoelastic model of solvent with a single relaxation time. The theory pr edicts that at high frequencies the dynamic viscosity of such solutions is less than the zero-shear-rate solvent viscosity.