Part of any basis of a relatively free group\(F_r (\mathfrak{B})\) in the variety\(\mathfrak{B}\) is called a primitive system of elements. We provide a criterion of being primitive for\(F_r \left( {\mathfrak{A}_m \mathfrak{B}} \right)\), where\(\mathfrak{A}_m \) is a variety of Abelian groups satisfying xm=1, and\(\mathfrak{B}\) a variety generated by a finite group. Let\(\mathfrak{N}_c \) be a variety of nilpotent groups of class ≤c. It is proved that, for the group\(F_2 \left( {\mathfrak{A}\mathfrak{N}_2 } \right)\), the property of being primitive for an element g is stronger than the condition of being unimodular on a vector composed of values of Fox derivatives in the ring\(\mathbb{Z}F_2 \left( {\mathfrak{N}_2 } \right)\). The group\(F_2 \left( {\mathfrak{A}\mathfrak{N}_2 } \right)\) is not residually finite whenever a system of elements is primitive.