In this paper, we consider a two-machine re-entrant permutation flowshop scheduling problem with the objective of minimizing total flowtime, and suggest branch and bound algorithms for the scheduling problem. In this scheduling problem, each job must be processed twice on each machine, that is, each job should be processed on the two machines in the order of machine 1, machine 2 and then machine 1 and machine 2. In this research, based on the results of existing researches for re-entrant permutation flowshop scheduling problems, various dominance properties, lower bound and heuristic algorithm are suggested for the problem, and those are used to develop branch and bound algorithms. In the computational experiments for evaluation of the performance of the algorithms, the suggested branch and bound algorithms are tested on randomly generated test problems and results are reported.