In this study, we focus on the inference presupposed in the concessive discourse relation and present the discourse relation annotation for the Japanese connectives ‘nagara’ and ‘tsutsu’, both of which have two usages: Synchronous and Concession, just like English while. We also present the annotation for ‘tokorode’, which is ambiguous in three ways: Temporal, Location, and Concession. While corpora containing concessive discourse relations already exist, the distinctive feature of our study is that it aims to identify the concessive inferential relations by writing out the implicit presupposed inferences. In this paper, we report on the annotation methodology and its results, as well as the characteristics of concession that became apparent during annotation.