The recent developments in the regular language theory motivate us to study classes of homomorphisms from free monoids onto monoids. Such objects can be treated as a pairs (M, A) where M is a monoid and A is a subset of M generating M. This generalizes the classical universal algebra. In our case we consider the so-called literal varieties of homomorphisms onto groups. These are given as classes which satisfy a given set of identities literally : in the identity u(x1, ..., xn)=v(x1, ..., xn) we substitute only elements of A for variables. In case of abelian groups the proper literal varieties are exactly the classes given by literal satisfaction of pairs x^k=y^k, x^l=1, k divides l - known. In our contribution we will solve the case of nilpotent groups of class at most 2 and we will also present the corresponding languages.