2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98744We generalize the notion of hyperquasivariety and hyperquasiidentity to the notion of M-hyperquasivariety and M-hyperquasiidentity. Birkhoff's and Malcev's type theorems are presented.The paper was presented at AAA69 Workshop on General Algebra, Potsdam, March 18-20, 2005. Accepted for publication in Demonstratio MathematicaGeneral MathematicsLogic08C15, 08C99text