  In this paper we study smooth orientation-preserving free actions of the
cyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds,
$\sharp g (S^n \times S^n)\sharp \Sigma$, where $\Sigma$ is a homotopy
$2n$-sphere. When $n=2$ we obtain a classification up to topological
conjugation. When $n=3$ we obtain a classification up to smooth conjugation.
When $n \ge 4$ we obtain a classification up to smooth conjugation when the
prime factors of $m$ are larger than a constant $C(n)$.
