In this paper we show how Maximum Likelihood Sequence Estimation (MLSE) can be implemented in a Linear Periodic Time-VaryingMultiple Access (LPTVMA) system. Assuming quasi-synchronous users, LPTVMA systems can be considered as Multi User Interference (MUI) free systems. Hence LPTVMA systems can be equalized. In multipath channels the equalization step uses a Zero Padding (ZP) technique. The equivalent channel to equalize is a zero-pad channel. For such zero-pad channels the MLSE can be efficiently implemented by using a parallel trellis Viterbi algorithm. The complexity of the MLSE can be further reduced because the padding zeros have known positions in the received signal. The proposed MLSE uses a periodic time-varying trellis. Thus the number of states of the MLSE can be reduced. The performances of LPTVMA systems using the proposed MLSE are evaluated by simulations.