Here we initiate an investigation into the class $mL{M}_{n\times m}$ of monadic $n\times m$-valued Łukasiewicz-Moisil algebras (or $mL{M}_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$-valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $mL{M}_{n\times m}$ is a discriminator variety and as a consequence, the...