  We explore four-dimensional Einstein-Weyl gravity and supergravity on anti-de
Sitter spacetime. For a specific range of the coupling with appropriate
boundary conditions, we show the effective equivalence of the theory with
Einstein gravity and AdS supergravity at the quadratic Lagrangian level.
Furthermore we show that these equivalences can be promoted to the full
nonlinear level. We also show that the similar behavior holds for the
generalized Gibbons-Hawking terms. From this we find that the correlation
functions in the dual conformal field theory of Einstein-Weyl gravity and
supergravity can be readily read off from corresponding ones from Einstein
gravity and AdS supergravity. We also give comments on some issues in critical
gravity and supergravity as well as conformal gravity and supergravity.
