In recent years, many studies on the multi-agent scheduling problems in which agents compete for using the shared resources, have been performed. However, relatively few studies have been undertaken in the field of the multi-agent scheduling in a flowshop environment. To bridge the gap, this paper aims at addressing the two-agent scheduling problem in a two-machine flowshop. Because of the importance of delay penalties and efficient resource utilization in many manufacturing environments, the objective is to find an optimal schedule which has the minimum total tardiness for the first agent’s jobs, under the makespan limitation for the second agent. Since this problem is strongly NP-hard, several theorems and properties of the problem are proposed to apply in exact and meta-heuristic methods. Also, for some instances of the problem for which exact methods cannot achieve optimal solutions in a reasonable amount of time, a tabu search algorithm is developed to achieve near-optimal solutions. Computational results of the tabu search algorithm show that the average absolute error value is lower than 0.18 percent for instances with 20 to 60 jobs in size.