We report on three experiments that aim at measuring the role of prosody in the acceptability and interpretation of discourse relations between utterances connected by two French discourse markers, viz. "et" "and" and "alors" "then/well." These two discourse markers are highly polyfunctional: "et" "and" can express relations of "addition," "specification," "temporality," or "consequence," whereas "alors" "then/well" can express relations of "consequence," "specification," "concession," or "topic-shift," among others. The first experiment compares the naturalness of the stimuli in their spoken and written versions. The second experiment uses a forced-choice task where two prosodic versions of the same stimulus are confronted. The third experiment tests whether the prosody of the first segment and of the marker projects the discourse relation continuation. Our results show that the impact of prosody varies across markers and relations, with "alors" displaying stronger prosodic profiles associated to the discourse relations it introduces.