Several analyses of intraspecific animal communication have suggested that threat displays must convey reliable information about the abilities of the signaller in order to be evolutionarily stable. In this paper, a game-theoretic model shows that bluffing by animals of low fighting ability can persist as a profitable tactic in a stable communication system. It is assumed that use of the threat display depends upon variation in fighting ability that is not visible to the opponent and that there is a fitness cost, or ''handicap'', paid by animals that threaten and subsequently lose. Analysis of the model shows that a handicap is necessary for stable communication and that the effectiveness of the threat increases with the magnitude of the handicap. However, the handicap does not ensure fully reliable communication and bluffing always forms part of the evolutionarily stable strategy (ESS). At the ESS, the very strongest and the very weakest members of the population threaten, while animals of intermediate strength do not. This is possible because, although weaker animals are liable to greater handicaps when they signal, they also gain greater benefits than strong animals using the same display. If all animals that threaten pay the handicap regardless of the outcome of the fight, then there is no ESS. These results provide a possible explanation for bluffing by the stomatopod crustacean, Gonodactylus bredini, a species in which animals weakened by molting successfully repulse stronger opponents by use of threat displays.