Abstract We model,speculative behaviors,in a market,with …nite horizon,and complete information, where all traders are aware to be in a bubble. We introduce par- tially sophisticated investors, who understand only the aggregate selling and buying strategies of other traders along the bubble, without a precise understanding of the timing of these decisions. In the bubble equilibrium, such investors keep their positions in the speculative market for too long, since a series of high prices lead them,to overestimate,the duration,of the bubble. Fully rational investors ride the bubble and exit just before the crash. We show,that a bubble is more,likely to arise and to be longer the greater is the mass,of people who,can potentially enter the speculative market,relatively to those who,have already,invested in such market. We also show,that increasing the share of fully rational investors need not make the bubble disappear. First, a minimal mass of fully rational investors is needed to make,other investors aware that the crash is about,to occur and it is time to sell. Second, if agents are risk averse, bubbles may last longer when the amount of fully rational traders increases, since rational investors bear less risk and they may be willing to take longer positions in the speculative market. Keywords: speculative bubbles, bounded rationality.