The paper determines the performance of TCP when it is employed over a differentiated services network where ATM switches are used as label switching routers, as in Request for Comments 3035. A packet discard scheme is also evaluated with the goal of classifying incoming data flows in different levels of quality of service. In particular, assured forwarding in differentiated services per-hop-behavior, as reported in RFC 2597, is considered as reference scenario. Different degrees of quality of service imply different portions of bandwidth and levels of packet loss for data flows which share the same output link. TCP performance is investigated for low drop precedence flows, or high priority flows, when the considered packet discard scheme is employed during congestion intervals. Numerical results are reported and discussed for different levels of congestion.