  Conformal properties of the topological gravitational terms in $D=2$, $D=4$
and $D=6$ are discussed. It is shown that in the last two cases the integrands
of these terms, when being settled into the dimension $D-1$ and multiplied by a
scalar, become conformal invariant. Furthermore we present a simple covariant
derivation of the Paneitz operator in $D=4$ and formulate two general
conjectures concerning the conformal properties of topological structures in
even dimensions.
