  The variety of nilpotent groups is Noetherian. That is why two nilpotent
class s groups are geometrically equivalent if and only if they have same
quasi-identities ([Pl3]). Therefore, we can describe classes of geometrical
equivalence of nilpotent groups instead of describing quasivarieties generated
by single nilpotent group. The problem of geometrical equivalence can be
researched by the technique of approximation of groups ([Pl2]). In this paper
only nilpotent torsion free groups are considered. In the first part two
sufficient conditions are presented (Theorem 1 and Theorem 2) when the
nilpotent torsion free group is geometrically equivalent to its Mal'tsev
completion and so it belongs to the same quasi-variety. In the second part of
this paper some results are achieved by the easy methods of approximation of
groups in the describing of classes of geometrical equivalence of nilpotent
class 2 torsion free groups with the small rank of center.
