We shall take for granted the basic terminology currently in use in the theory of varieties of groups. Kovács, Newman, Pentony [2] and Levin [3] prove that if m is an integer greater than 2, then the variety Νm of all nilpotent groups of class at most m is generated by its free group Fm-1(Νm) of rank m – 1 but not by its free group Fm–2(Νm) of rank m — 2. That is, the free groups Fk(Nm), 2≦k ≦ m – 2, do not generate Nm. In general little is known of the varieties generated by them. The purpose of the present paper is to record the varieties of the free groups Fk(Nm) of the nilpotent varieties Nm of all nilpotent groups of class at most m for 2 ≦ k ≦ m – 2 and 5 ≦ m ≦ 6. This is done by describing a basis for the laws in these groups, that is a set of laws the fully invariant closure of which is the set of all laws for Fk(Nm). The set of laws, which, together with the appropriate nilpotency law, form a basis for the relevant groups Fk(Nm) are listed below: .