We consider a network model where bandwidth is fairly shared by a dynamic number of elastic and adaptive streaming flows. Elastic flows correspond to data transferts while adaptive streaming flows correspond to audio/video applications with variable rate codecs. In particular, the former are characterized by a fixed size (in bits) while the latter are characterized by a fixed duration. This flow-level model turns out to be intractable in general. In this paper, we give performance bounds for both elastic and streaming traffic by means of sample-path arguments. These bounds present the practical interest of being insensitive to traffic characteristics like the distribution of elastic flo size and streaming flow duration.