While corpus studies have shown that discourse connectives that convey the same coherence relation can display subtle differences, research on online discourse processing has only focused on a rather limited set of connectives. Yet, different connectives – for example, rare or polyfunctional ones – might elicit different reading patterns. In order to explore this assumption, we test the robustness of discourse processing for French native speakers by measuring the way they process causal and concessive sentences that are conveyed by either (...) an appropriate or inappropriate connective. Throughout three experiments, we change important characteristics of the connectives: we first test frequently used connectives, secondly less frequent ones, and finally less frequent connectives that are polyfunctional and for which different functions clearly compete. Our results show that the processing for incoherent items was affected for all connectives, however readers showed altered reading fluency when infrequent connectives were used. We conclude that discourse processing is quite robust and that readers are able to insert meaning conveyed by rare connectives while still showing the highest reading ease with frequent connectives. (shrink)