The maturation of Xenopus oocytes can be thought of as a process of cell fate induction, with the immature oocyte representing the default fate and the mature oocyte representing the induced fate. Crucial mediators of Xenopus oocyte maturation, including the p42 mitogen-activated protein kinase (MAPK) and the cell-division cycle protein kinase Cdc2, are known to be organized into positive feedback loops. In principle, such positive feedback loops could produce an actively maintained `memory' of a transient inductive stimulus and could explain the irreversibility of maturation. Here we show that the p42 MAPK and Cdc2 system normally generates an irreversible biochemical response from a transient stimulus, but the response becomes transient when positive feedback is blocked. Our results explain how a group of intrinsically reversible signal transducers can generate an irreversible response at a systems level, and show how a cell fate can be maintained by a self-sustaining pattern of protein kinase activation.