We present some problems against due dates with past sequence dependent setup times under learning effect and linear deterioration effect. In this study, effects of learning and deterioration are considered simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. In the past sequence dependent setup times approach, the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. In this study, we demonstrated that some problems with due dates remain polynomially solvable. However, for some other problems, we concentrated on finding polynomially solvable under their special cases.