Since the fitness consequences of mate desertion are markedly affected by whether the partner also deserts, natural selection is expected to favour desertion decisions that take the mate's decision into account. A model for the evolution of mate desertion is described in which individuals make desertion decisions repeatedly during the period of parental care, choosing the option (desert or stay) that gives them the greater fitness, taking into account whether their mate has already deserted. If the partner still remains, the optimal decision is made assuming that the partner responds optimally in turn. Four patterns of time-dependent payoffs define all possible desertion decisions, three of which produce different kinds of stable evolutionary outcome: both parents stay with the young; both desert; and one deserts, one stays. The fourth pattern ('pre-emptive desertion') also results in both parents deserting but paradoxically, in this case, they sacrifice fitness by so doing. Such uncooperative parents are caught in the well-known Prisoner's Dilemma of game theory and provide a link with recent thinking on the evolution of cooperation. Under conditions of mate choice or repeated interaction between potential mates the payoff pattern that normally produces pre-emptive desertion may result instead in a 'both stay' outcome. When desertion decisions are conditional on the partner's decision, in the way assumed here, desertion outcomes cannot be predicted simply by comparing the costs and benefits of desertion for the male and female at any one time. Rather, one needs to know the way in which these payoffs vary for each partner over the whole of the parental care period. Applications of the model are discussed, with particular reference to uniparental care in fish and biparental care in birds. © 1990.