The current transients induced by a potential step at a microband electrode located in a rectangular channel through which solution is pumped under laminar flow conditions are described by theory which accounts for convection axially through the flow cell and diffusion normal, and parallel, to the electrode surface. The hopscotch algorithm is used to predict numerically the form of the chronoamperometric transients as a function of the flow cell/electrode geometries and as a function of flowrate. Experiments are reported for the reduction of p-chloranil in acetonitrile solution using gold channel microbands : the effect of electrode size and solution flow rate is found to be in excellent agreement with the theoretical predictions. Computed concentration profiles showing the depletion of the electroactive material as a function of time after a potential step are presented and reveal that axial diffusion leads to significant depletion of material at large distances upstream of the electrode.