  For commutative Euclidean time, we study the existence of field
configurations that {\it a)} are formal power series expansions in
$h\theta^{\m\n}$, {\it b)} go to ordinary (anti-)instantons as
$h\theta^{\m\n}\to 0$, and {\it c)} render stationary the classical action of
Euclidean noncommutative SU(3) Yang-Mills theory. We show that the
noncommutative (anti-)self-duality equations have no solutions of this type at
any order in $h\theta^{\m\n}$. However, we obtain all the deformations --called
first-order-in-$\theta$-deformed instantons-- of the ordinary instanton that,
at first order in $h\theta^{\m\n}$, satisfy the equations of motion of
Euclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantum
effects that these field configurations give rise to in noncommutative SU(3)
with one, two and three nearly massless flavours and compute the corresponding
't Hooft vertices, also, at first order in $h\theta^{\m\n}$. Other issues
analyzed in this paper are the existence at higher orders in $h\theta^{\m\n}$
of topologically nontrivial solutions of the type mentioned above and the
classification of the classical vacua of noncommutative SU(N) Yang-Mills theory
that are power series in $h\theta^{\m\n}$.
