Testing for rational bubbles in financial asset prices has proven to be difficult. A cite quote from Gürkaynak (J. Econ. Surveys, 2008) states: “For each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble”. In the context of the simple stock price model it has been suggested that a rational bubble cannot be distinguished from the fundamental price. We show that this assertion is true not only for the stock price model but for any fundamental price that is determined by arbitrage arguments. In particular, bubbles defined as processes with explosive conditional mean -which is standard in the financial literature- are identified only on a set of null probability. More in general, because identification of rational bubbles is symmetric to the identification of the fundamental price, the latter requires the characterization of some identifying restrictions, which take the form of necessary transversality conditions (NTCs) for the respective price model. NTCs for the class of Markov and Harrison recurrent price processes are derived.