  We study some subgroups of the group of unitriangular automorphisms $U_n$ of
a free associative algebra over a field of characteristic zero. We find the
center of $U_n$ and describe the hypercenters of $U_2$ and $U_3$. In
particular, we prove that the upper central series for $U_2$ has infinite
length. As consequence, we prove that the groups $U_n$ are non-linear for all
$n \geq 2$.
