  This paper belongs to a series of papers devoted to the study of the
structure of the non-wandering set of an A-diffeomorphism. We study such set
$NW(f)$ for an $\Omega$-stable diffeomorphism $f$, given on a closed connected
3-manifold $M^3$. Namely, we prove that if all basic sets in $NW(f)$ are
trivial except attractors, then every non-trivial attractor is either
one-dimensional non-orientable or two-dimensional expanding.
