Brownian dynamics simulations are performed for salt-free polyelectrolyte solutions with divalent counterions. The polymer molecules are modeled as freely jointed charged chains and the counterions are incorporated explicitly. The conformational properties, static structure, and dynamic properties of salt-free polyelectrolyte solutions show interesting behavior that can be attributed to the correlations induced by the counterions. The size of polyelectrolyte chains and the counterion self-diffusion coefficient show a nonmonotonic concentration dependence. There is a sharp peak in the polyion pair correlation functions at short distances and an upturn in the partial static structure factors at low wave vectors. In semidilute solutions, the polyions contract in the presence of divalent counterions, when compared to solutions with monovalent counterions. This contraction is accompanied by the peak in the static structure moving to lower wave vectors. The self-diffusion of polyions is faster with divalent counterions than with monovalent counterions, whereas the collective diffusion at long length scale slows down with divalent counterions compared to the monovalent case. These results are consistent with experiments and suggest that primitive models with strong electrostatic correlations can explain many of the experimental observations. (C) 2003 American Institute of Physics.