In this paper we propose a Markovian model of BitTorrent. Unlike already developed works which capture demographic dynamics, it focuses on the behavior of individual peers. To this end, we center our attention on a generic peer, called tagged peer (TP); for each possible logical state of a BT peer-to-peer connection maintained by the TP, we consider a stochastic process which counts the number of such links, and characterize them according to their state. Validation is carried out and steady-state analysis is performed in order to illustrate how performance evaluation can be extracted from our model.