We use dynamic light scattering to measure the dynamic structure facto
r of density fluctuations occurring in colloidal suspensions that have
attained a quiescent state long after aggregation. We find a stretche
d-exponential decay to a finite plateau. Our interpretation of the arr
ested decay is that these systems are gels, i.e., systems possessing a
finite elastic modulus G. We develop a theory for the internal elasti
c modes of a fractal cluster and use it to derive G and the arrested,
stretched-exponential behavior of colloidal gel dynamics. Good agreeme
nt between experiment and theory is obtained.