The magnetic behavior of the mixed spin-1 and spin-3/2 Ising system on a bilayer square lattice is studied using the Monte Carlo simulations for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromag netic interactions in the presence and absence of external magnetic, crystal field and for different values of exchange interactions. The thermal variations of the magnetizations are given. The magnetic hysteresis cycles are established. The magnetic coercive field and the remanent magnetization are deduced. The coercive magnetic field, remanent magnetization and the transition temperature were not affect by the size effect. (C) 2016 Elsevier B.V. All rights reserved.