This note relates to the study of Hamilton and Slutsky ((1990) Games Econ. Behav. 2, 29-46) on endogenous timing (with observable delay). It shows, via counterexample, that monotonicity of the best-reponse functions in a two-player game is not sufficient to derive predictions about the order of moves. Rather, this requires, additionally, the monotonicity of each payoff in the other player's actions. Journal of Economic Literature Classification Numbers: C72, L10. (C) 1995 Academic Press, Inc.