  The singular part of the \textit{operator product expansion} (OPE) of a pair
of \textit{globally conformal invariant} (GCI) scalar fields $\phi$ of
(integer) dimension $d$ can be written as a sum of the 2-point function of
$\phi$ and $d-1$ bilocal conformal fields $V_{\nu}(x_1, x_2)$ of dimension
$(\nu, \nu)$, $\nu = 1, ..., d-1$. As the correlation functions of $\phi(x)$
are proven to be rational [6], we argue that the correlation functions of
$V_{\nu}$ can also be assumed rational. Each $V_{\nu}(x_1, x_2)$ is expanded
into local symmetric tensor fields of \textit{twist} (dimension minus rank)
$2\nu$. The case $d=2$, considered previously [5], is briefly reviewed and
current work on the $d=4$ case (of a Lagrangean density in 4 space--time
dimensions) is previewed.
