  Let $c\geq 0$, $d\geq 2$ be integers and $\mathcal{N}_c^{(d)}$ be the variety
of groups in which every $d$-generator subgroup is nilpotent of class at most
$c$. N.D. Gupta posed this question that for what values of $c$ and $d$ it is
true that $\mathcal{N}_c^{(d)}$ is locally nilpotent? We prove that if $c\leq
2^d+2^{d-1}-3$ then the variety $\mathcal{N}_c^{(d)}$ is locally nilpotent and
we reduce the question of Gupta about the periodic groups in
$\mathcal{N}_c^{(d)}$ to the prime power finite exponent groups in this
variety.
