  We prove a homological stability theorem for moduli spaces of
high-dimensional, highly connected manifolds, with respect to forming the
connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p
- 2$. This result is analogous to recent results of S. Galatius and O.
Randal-Williams regarding the homological stability for the moduli spaces of
manifolds of dimension $2n > 4$, with respect to forming connected sums with
$S^{n}\times S^{n}$.
