A polystyrene-poly(ethylene-alt-propylene) diblock copolymer, S/EP 7/13, exhibits a thermoreversible mesophase transition between low-temperature hexagonally perforated lamellae (HPL) and high-temperature hexagonally packed cylinders (C). The transformation process is accompanied by a 6% change in the principal spacing, yet oriented specimens retain their macroscopic orientation through the transition. The C -> HPL transformation proceeds on a time scale of tens of minutes, at a rate which initially increases rapidly with undercooling relative to the order-order transition temperature. At deep undercoolings, the transformation rate slows due to a reduction in molecular mobility, By contrast. the HPL -> C transformation occurs nearly 2 orders of magnitude more rapidly,a difference which is suggested to reflect the nature of the dominant fluctuation modes for the two structures.