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The phenomenon of overtaking in queueing systems and queueing networks has been addressed by several authors with various motivations in the last decades. Nevertheless, up to now, for the relatively simple M/M/2/FCFS queue, the distribution of the number of overtakes a stationary customer suffers from was not known. In this paper, we characterize this distribution by its probability generating function. As a consequence, we derive the expectation (which is well-known) and the variance. Keywords: Queueing, Overtakes, Absorbing Markov chain, MSC: 60K25, 68M20, 60J10