Let $(M,g)$ be an $n/ge 5$ dimensional smooth compact Riemannian manifold of positive Yamabe type, which is not conformally equivalent to the standard sphere.  We prove compactness of conformal metrics of $g$ with positive constant Q-curvature provided that $(M,g)$ is locally conformally flat, or $5/le n/le 9$. We also prove the compactness result in dimension $n/ge 8$, provided that the Weyl tensor of $g$ does not vanish anywhere.