Looking for a better understanding of spontaneous speech-related phenomena and to improve automatic speech recognition (ASR), we present here a study on the relationship between the occurrence of overlapping speech segments and disfluencies (filled pauses, repetitions, revisions) in political interviews. First we present our data, and our overlap annotation scheme. We detail our choice of overlapping tags and our definition of disfluencies; the observed ratios of the different overlapping tags are examined, as well as their correlation with of the speaker role and propose two measures to characterise speakers' interacting attitude: the attack/resist ratio and the attack density. We then study the relationship between the overlapping speech segments and the disfluencies in our corpus, before concluding on the perspectives that our experiments offer.