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In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class ${}_{n\times m}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM${}_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil...