We examine the configurational phase transitions of flexible polymer chains in planar mixed flows. We distinguish three distinct phases: the coiled state (C) in which the flow is unable to deform the chain significantly from its equilibrium configuration, the tumbling state (T) in which the chain undergoes a tumbling motion and the chain fluctuations are comparable to the full chain contour length as in shear flow, and the fully stretched state (S) in which the chain is fully stretched in its steady configuration and the chain fluctuations are small compared to the full chain contour length as in extensional flow. As the mixed flow parameter alpha changes, the chain undergoes changes in configuration from C to T to S. We consider separately the phase transitions from C to T (C-T) and from T to S (T-S). We use physical arguments and supporting Brownian dynamics simulations to derive the range in the parameter alpha (as a function of the flow strength Wi and chain molecular weight N) over which such phase transitions occur in the high flow strength limit. (C) 2003 American Institute of Physics.