The motion of probe particles in aqueous solutions of linear and branched poly(vinyl alcohol) (PVA) and in chemically cross-linked PVA gels has been studied by diffusing-wave spectroscopy. At long time scales the measurements allow to determine the effect of the cross-linking ratio on the macroscopic viscosity of sols and the shear modulus of gels. The local shear modulus of gels as obtained from the characteristic length of the Brownian cage was found to agree with that measured by classical rheometry and dynamic light scattering. The behavior of the mean-square displacement of the probe particles at short time indicates that the high-frequency viscoelasticity is the same for solutions and highly crosslinked gels whereas gels with low cross-linking ratio exhibit a lower storage modulus.