For an arbitrary class of groups M we denote by L(M) the class of all groups G where the normal closure of every element of G belongs toM. The class L(M) is called a Levi class generated by M. Levi classes were introduced under the influence of a paper by F. Levi with the classification of groups with abelian normal closures. R.F. Morse proved that if the class M is a variety of groups, then L(M) is also a variety of groups. From the works of A.I. Budkin it follows that if M is a quasivariety of groups, then L(M) is a quasivariety of groups, too. Earlier we found descriptions of the Levi classes generated by the almost Abelian quasivarieties of nilpotent groups (except one). In this article, we continue to investigate the Levi classes. It is proved that for a locally finite variety of groups M, Levi class generated by M is also a locally finite variety. We describe subdirectly irreducible groups of Levi class generated by the variety of groups of exponent 2ρ with the commutant exponent ρ, in which squares of elements are commuting (ρ is a prime, ρ ≠ 2, 3). Also, we demonstrate that any group of Levi class generated by the variety of groups of exponent 2ρ with the commutant exponent ρ, in which squares of elements are commuting (ρ is a prime, ρ ≠ 2), is a 3-metabelian group.