The paper is devoted to the statistical analysis of VoIP traffic generatedby Skype users. In our paper we focus on the statistical characterization of single Skype flows. We investigate the stationarity, long-range dependence,self-similarity and heaviness of tails of the distributionsof the inter-arrival times and lengths processes of voice packets arising from aunidirectional Skype packet stream. We show that simple recurrentor weakly correlated marked point processes with light-tailed inter-arrival times and independently marked packetsizes that have been derived for voice traffic with constant bit rate encodingand their ramifications cannot be applied to these new traffic flows.