The nonlinear viscosity of the wormlike surfactant system cetyl pyridinium chloride/sodium salicylate (60 mM/100 mM in water) has been investigated in both pipe and cylindrical Couette geometries, using nuclear magnetic resonance to image both velocity and diffusion. In pipe flow we observe transitions from Newtonian to non-Newtonian viscosity, to spurt, to unstable flow, and then to a regime where fluctuations are rapid on the timescale of a few milliseconds. In the Couette cell we observe apparent slip at the inner wall as well as a high shear rate band located away from the wall in the body of the fluid. The banding phenomenon, which has its counterpart in the pipe flow, is consistent with double valuedness in the stress versus rate of strain relationship for this fluid.