Over the last few years, peer-to-peer (P2P) file sharing applications have evolved to become a major traffic source in the Internet. The ability to quantify their impact on the network, as a consequence of both signaling and download traffic, is fundamental to a number of network operations, including traffic engineering, capacity planning, quality of service, forecasting for long-term provisioning, etc. We present here a measurement study on the characteristics of the traffic associated with different P2P applications. Our aim is to offer useful insight into the nature of P2P traffic, which we consider a step toward building P2P traffic aggregates generators in simulative environments. We show that P2P traffic can be divided into two distinguished behavioral profiles, which, independently of the application protocol, present significant differences in the average and standard deviation of four measurements: arrival times, durations, volumes and average packet sizes of P2P conversations. These profiles well represent the typical behavior of signaling and download traffic. Based on our findings, we argue that, if such distinction is not taken into account, the statistical measurements needed to model P2P traffic aggregates would result biased, and potentially bring to misleading results.