In this paper a statistical analysis of real ATM traffic is considered to validate the presence of long range dependence (LRD) in a set of telecommunication networks and protocols wider than those examined so far in the literature. The data come from a measurement campaign conducted in Italy by Telecom Italia in the framework of the European ATM Pilot Project. The notions of self similarity, LRD, second order self similarity are revised thoroughly, and the criteria for identifying the presence of LRD are presented. The available measurements (the applications considered are videoconference and transport of routing information between IP network routers) are processed through heuristic (R/S statistic, sampling variance plot, correlogram) as well as semiparametric (the Whittle estimator) techniques. The analysis shows that (i) evidence of LRD is statistically significant in the IP routing protocol application; (ii) the heuristic methods currently considered to detect LRD may not be able to capture the nature of the available data. These findings suggest to investigate further the impact of LRD in engineering and performance evaluation of ATM and IP networks, and to explore deeply the use of other semiparametric methods for the analysis of long memory sequences.