Velocity dispersion as a function of radius, called sigma/sub ls/ profiles, is presented for 13 clusters of galaxies having > or =30 radial velocities from both published and unpublished lists. A list of probable new members and possible outlying members for these clusters is also given. chi/sup 2/ and Kolmogoroff--Smirnoff one-sample tests for the goodness of fit of power laws to portions of the profiles indicate two significant structures in some profiles: (1) a local minimum corresponding to the local minimum noted in surface density or surface brightness profiles, and (2) a decrease in sigma/sub ls/ toward the cores. Both of these features are discussed in terms of a comparison with Wielen's N-body simulations. The sigma/sub ls/ profiles are placed in a new classification scheme which lends itself to interpreting clusters in a dynamical age sequence. The velocity field of galaxies at large distances from cluster centers is also discussed.