In most of the scheduling researches, it is assumed that machines are available continuously. But in the real world, the available times of machines is restricted by some reasons like breakdowns, planning horizon overlaps, tool change and maintenance activities. Scheduling problems with availability constraint are justify; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr" Start time, finish time and the duration of unavailability period are previously known in problems with fixed availability constraint. On the other hand, in the case of problems with flexible availability constraint, the duration of unavailability period is previously known but its start time is a decision variable. In some problems of this group, a fixed time-interval is considered for availability constraint while in others, the maximum continuous working time of the machine is determined. Also in problems with variable availability constraint, the duration of unavailability period depends on machine and operator’s conditions. In researches on variable availability constraint, the amount of deterioration effect on processing times, determines start time and duration of machine stopping time. In the literature, single machine scheduling problem with fixed availability constraint is considered in many cases. But single machine scheduling problem with flexible availability constraint is considered less than fixed type. In this study, we focused on a novel definition of availability constraint called bimodal flexible and periodic maintenance activities. In this definition, in each period, the maximum continuous working time of a machine could have two values and so duration time of maintenance could have two values. First, a justify; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr" In the rest of this study, the single machine scheduling problem with bimodal flexible and periodic maintenance activities is investigated to minimize total completion times. The problem is proved to be NP-Hard. A heuristic algorithm called BLCB with O(n logn) time complexity and a back-tracking branch and bound algorithm with a lower bound and dominance properties is developed. The solution of heuristic algorithm is used as an upper bound in branch and bound algorithm. Computational results on 1680 problem instances shows that the branch and bound algorithm can solve 98.39 percent of problems with up to 22 jobs and the average error of the heuristic algorithm is equal to 1.05 percent. In the next section of this study, single machine scheduling problem with bimodal flexible and periodic maintenance activities is investigated to minimize the number of tardy jobs. Like the previous section, this problem is also proved to be NP-Hard and a heuristic algorithm called H 2 with O(n logn) time complexity proposed. Then a back-tracking branch and bound algorithm concluding some lower bounds, dominance properties and the solution of H 2 as upper bound is proposed and tested. Computational results on 1680 problem instances shows that the branch and bound algorithm can solve 94.76 percent of problems with up to 20 jobs and the average error of heuristic algorithm is equal to 2 percent.