  Two and three point functions of composite operators are analysed with regard
to (logarithmically) divergent contact terms. Using the renormalisation group
of dimensional regularisation it is established that the divergences are
governed by the anomalous dimensions of the operators and the leading
UV-behaviour of the $1/\epsilon$-coefficient. Explicit examples are given by
the $<G^2G^2>$-, $<\Theta \Theta>$-trace of the energy momentum tensor) and
$<\bar q q \bar q q>$- correlators in QCD-like theories. The former two are
convergent when all orders are taken into account but divergent at each order
in perturbation theory implying that the latter and the the $\epsilon \to 0$
limit do not generally commute. Finite correlation functions obey unsubtracted
dispersion relations which is of importance when they are directly related to
physical observables. As a byproduct the $R^2$-anomaly is extended to NNLO
($O(\alpha^5)$) using a recent $<G^2G^2>$-computation.
