Knowledge of the conformational evolution of a polymer chain provides invaluable information for all polymer properties. However, the chain evolution is usually determined by monitoring single beads for short times only. In this paper, we numerically determine the configuration evolution over extended time periods by monitoring the eigenvalues of the gyration tensor and applying the scaling law methodology. Results of Brownian dynamics simulations of initially straight chains reveal that after the early free transverse diffusion, flexible polymers exhibit a transverse intermediate-time behavior of t(3/4), while stiff polymers reveal two intermediate-time behaviors: an early t(5/6) power law accompanied by a late t(3/4) evolution. These results are associated with the inherent nonlinearity of the problem. The scaling law methodology we develop in this paper for monitoring the chain configuration should have wide applications in the study of polymer rheology. (C) 2003 American Institute of Physics.