The motion of probe particles in aqueous solutions of linear and branched p
oly(vinyl alcohol) (PVA) and in chemically cross-linked PVA gels has been s
tudied by diffusing-wave spectroscopy. At long time scales the measurements
allow to determine the effect of the cross-linking ratio on the macroscopi
c 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 part
icles at short time indicates that the high-frequency viscoelasticity is th
e same for solutions and highly crosslinked gels whereas gels with low cros
s-linking ratio exhibit a lower storage modulus.