Bubbles in asset prices have fascinated researchers in finance. Identify asset bubbles, by circumstances, on the stock market has been a growing number of research theoretical and empirical. On a theoretical level, it was assumed that the price dynamics reflect irrational behavior of economic agents and, therefore, should be excluded from a deal with the truly rational economic agents Burmeister [1980], Cass and Shell [1983] , Tirole [1985] and Diba & Grossman [1988]. Rational theory and behavioral theory attempted to explain why bubbles occur Allen and Gale [2000] Abreu & Brunnermeier [2003], Scheinkman and Xiong [2003] and Men [2006]. This paper examines the presence of rational speculative bubbles in the Tunisian equity market (BVMT) over a sample period from January 2000 to December 2013 by means of a methodology based on a non-parametric duration dependence test. The results show evidence of negative duration dependence in runs of positive returns, a characteristic consistent with the presence of rational speculative bubbles. This paper employs the generalized Weibull model of Mudholkar, Srivastava, and Kollia (1996) to examine the nature of speculative bubbles in security prices. This model is sufficiently flexible to allow changes in the direction of duration dependence تفاصيل المقالة