  We enumerate labelled and unlabelled Hamiltonian cycles in complete
$n$-partite graphs $K_{d,d,\ldots,d}$ having exactly $d$ vertices in each part
(in other words, Tur\'an graphs $T(nd, n))$. We obtain recurrence relations
that allow us to find the exact values $b_{n}^{(d)}$ of such cycles for
arbitrary $n$ and $d$
