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Recently peer-to-peer (P2P) configurations have found considerable interest in the Internet community. At the same time P2P has often been criticized for poor scaling behavior. We analyze P2P signaling traffic, both via analytic estimates and via computer simulation. With the help of two probabilistic approaches, we can derive an upper as well as a lower bound for the growth of P2P-signaling traffic, according to a pure peer-to-peer protocol as given e.g. in the Gnutella protocol. With the help of a simulation we are able to verify our mathematical derivations. As a result it appears, that P2P actually scales much better than predicted by more conventional theory relying on simplifying assumptions, and thus exponential growth of the messaging load in pure peer-to-peer networks must not be assumed.