In this paper, we make a qualitative and quantitative analysis of discourse relations within the LUNA conversational spoken dialog corpus. In particular, we describe the adaptation of the Penn Discourse Treebank (PDTB) annotation scheme to the LUNA dialogs. We discuss similarities and differences between our approach and the PDTB paradigm and point out the peculiarities of spontaneous dialogs w.r.t. written text, which motivated some changes in the sense hierarchy. Then, we present corpus statistics about the discourse relations within a representative set of annotated dialogs.