Wide availability of computing resources at the edge of the network has lead to the appearance of new services based on peer-to-peer architectures. In a peer-to-peer network nodes have the capability to act both as client and server. They self-organize and cooperate with each other to perform more efficiently operations related to peer discovery, content search and content distribution. The main goal of this thesis is to obtain a better understanding of the network traffic generated by Gnutella peers. Gnutella is a well-known, heavily decentralized file-sharing peer-to-peer network. It is based on open protocol specifications for peer signaling, which enable detailed measurements and analysis down to individual messages. File transfers are performed using HTTP. An 11-days long Gnutella link-layer packet trace collected at BTH is systematically decoded and analyzed. Analysis results include various traffic characteristics and statistical models. The emphasis for the characteristics has been on accuracy and detail, while for the traffic models the emphasis has been on analytical tractability and ease of simulation. To the author's best knowledge this is the first work on Gnutella that presents statistics down to message level. The results show that incoming requests to open a session follow a Poisson distribution. Incoming messages of mixed types can be described by a compound Poisson distribution. Mixture distribution models for message transfer rates include a heavy-tailed component.