  In this paper, we initiate the study of palindromic automorphisms of groups
that are free in some variety. More specifically, we define palindromic
automorphisms of free nilpotent groups and show that the set of such
automorphisms is a group. We find a generating set for the group of palindromic
automorphisms of free nilpotent groups of step 2 and 3. In particular, we
obtain a generating set for the group of central palindromic automorphisms of
these groups. In the end, we determine central palindromic automorphisms of
free nilpotent groups of step 3 which satisfy the necessary condition of
Bryant-Gupta-Levin-Mochizuki for a central automorphism to be tame.
