Laser Doppler velocimetry is used to measure velocities during the development from rest of circular Couette flow. Velocities are measured at two points in the fluid from the inception of the flow until the velocities reach steady state. Three test fluids are investigated, one Newtonian fluid and two viscoelastic solutions of polyisobutylene. In each of the two viscoelastic test fluids, a nearly discontinuous front in velocity propagates from the inner (rotating) cylinder out into the fluid. The speed of propagation is found to be approximately given by [ G(0)/ϱ] 1 2 , where G(0), the relaxation modulus at zero time difference, is determined by fitting complex viscosity data. Numerical calculations are also reported for the development of the velocity field and are compared to the experimental data. Good agreement is seen between the data and the calculations for a multimode Giesekus model with parameters fitted to complex viscosity, steady-state viscosity, and steady-state normal stress data for the test fluids. Calculations for a single mode model agree qualitatively with the data, but not as well as those for the multimode models.