It is commonly thought that the requirements of inferential justification are such that necessarily the process of inferentially justifying a belief will come to an end. But, If this is so, We should be able to pick out those requirements of justification which necessitate an end to the justification process. Unfortunately, Although there is nearly unanimous agreement as to the need for such an end, It is by no means clear which particular requirements of justification impose this need. I examine (...) and criticize several seemingly plausible ways of showing that regresses of inferential justification are impossible and then propose two requirements of inferential justification which, I argue, Are sufficient to show the impossibility. (shrink)