In this paper, we give two results concerning the positivity property of
the Paneitz operator-- a fourth order conformally covariant elliptic operator.
We prove that the Paneitz operator is positive for a compact Riemannian
manifold without boundary of dimension at least six if it has positve scalar
curvature as well as nonnegative $Q-$curvature. We also show that the positivity
of the Paneitz operator is preserved in dimensions greater than four in
taking a connected sum.