Brownian dynamics simulations are performed to study the stretching and transport of flexible polymers in complex electroosmotic flows. The flows are generated by prescribing a spatially periodic charge distribution on the walls of a parallel-plate channel and applying an electric field parallel to the direction of charge modulation. The polymer molecules are modeled as bead-spring chains and the model parameters are chosen to be representative of DNA. Simulations are performed for the cases of uncharged and charged polymers. For the uncharged case, it is found that the stagnation point in the center of the flow is not effective at stretching the polymers due to the fact that the flow has an inhomogeneous velocity gradient. It is observed that polymers tend to become trapped in the recirculation rolls near that stagnation point, and that the amount of stretching that does occur is directly proportional to the amount of time that the polymer spends near the stagnation point at the wall. For the charged case, it is found that the trapping persists below a critical charge density, but that above this threshold the polymer escapes from the rolls. Our observations suggest that while these complex flows may not be useful for stretching polymers far away from the channel walls, they may be useful for localizing the position of Brownian particles in microfluidic devices. In addition, they illustrate the rich dynamics that arise when polymers are placed in flows with inhomogeneous velocity gradients and when electroosmotic flow competes with electrophoresis. (C) 2003 American Institute of Physics.