In this paper, we propose a formal framework based on the Markov chains to prove the performance of P2P protocols. Despite the proposal of several protocols for P2P networks, sometimes there is a lack of a formal demonstration of their performance: experimental simulations are the most used method to evaluate their performance, such as the average length of a lookup. In this paper, we introduce a versatile model for the analysis of P2P protocols. We employ this model to formally prove which is the average lookup length for two sample protocols: BaRT and Koorde. We verify the effectiveness of the proposed framework also via extensive simulations.