  In this note we study the conformal metrics of constant $Q$ curvature on
closed locally conformally flat manifolds. We prove that for a closed locally
conformally flat manifold of dimension $n\geq 5$ and with Poincar\"{e} exponent
less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$
and positive scalar curvature is compact in the $C^\infty$ topology.
