This paper considers a two-machine re-entrant flowshop scheduling problem in which there are two classes of jobs with different urgencies, i.e., urgent jobs and normal (not urgent) jobs. The objective of this problem is minimizing total tardiness of one class of urgent jobs and maximum completion times of the other class of normal jobs. To solve this problem, a lower bound and several heuristic algorithms for the problem are proposed. To evaluate the performance of developed algorithms, computational experiments are performed on randomly generated problems, and results are reported with analysis. The suggested algorithms show better performances compared with the ones used in real manufacturing systems in terms of solution quality and computation time.