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In this paper, we consider a two parallel machine problem where each machine has a fixed and known unavailable period. The objective is to minimize the makespan. In the literature, the problem has been considered for the case in which there is only one unavailable period on either one of the machines. This paper extends the results to two unavailable periods, one for each machine. For each of the different cases of the problem, an algorithm is developed to find the optimal solution. Although all the proposed algorithms have exponential time complexities, they are quite efficient in solving large problems. Computational results for problems with up to 1000 jobs are reported. [ABSTRACT FROM AUTHOR]