In this paper, first we define the notion of an Engel polygroup, to get further properties on Engel fuzzy subpolygroups. Moreover, we prove that every normal fuzzy subpolygroup of an Engel polygroup is Engel. Furthermore, we introduce the notions of solvable and nilpotent fuzzy subpolygroups and we get some of their properties. Finally we investigate the relations among solvable and nilpotent fuzzy subpolygroups with Engel fuzzy subpolygroups.