In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. These lattices are divided in two interpenetrating sublattices with spins [Formula: see text] (states [Formula: see text] and 0) on the sublattice [Formula: see text] and [Formula: see text] (states [Formula: see text], [Formula: see text]) on the sublattice [Formula: see text]. We have used single-ion anisotropies [Formula: see text] and [Formula: see text] acting on the sites of the sublattice [Formula: see text] and [Formula: see text], respectively. We have determined the phase diagrams of the model in the temperature [Formula: see text] vs. the single-ion anisotropies strength [Formula: see text] and [Formula: see text] plane and shown that the system exhibits both second- and first-order phase transitions. This system also displays compensation points for some values of the anisotropies.

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