In this paper we present results about the presence of long-range dependence in on-chip processor traffic as well as a study of the impact of long-range dependence on networks-on-chip. Long-range dependence is a property of stochastic processes that has an important impact on network performance, especially on the buffer usage in the routers. From the exiting work of Varatkar and Marculescu, this property was evidenced in the communications between different elements of a mpeg hardware decoder at the macro-block level. In this paper we propose to investigate the presence of long-range dependence in communication traces of processor IPs at the cycle-accurate level. We also study practically the impact of long-range dependence on a real network-on-chip using SoCLib simulation environment and traffic generators of our own. Our experiments show that long-range dependence is not an ubiquitous property of on-chip processor traffic and that its impact on the network-on-chip performance is highly correlated to the low level communication protocol used.