  We discuss conserved currents and operator product expansions (OPE's) in the
context of a $O(N)$ invariant conformal field theory. Using OPE's we find
explicit expressions for the first few terms in suitable short-distance limits
for various four-point functions involving the fundamental $N$-component scalar
field $\phi^{\alpha}(x)$, $\alpha=1,2,..,N$. We propose an alternative
evaluation of these four-point functions based on graphical expansions.
Requiring consistency of the algebraic and graphical treatments of the
four-point functions we obtain the values of the dynamical parameters in either
a free theory of $N$ massless fields or a non-trivial conformally invariant
$O(N)$ vector model in $2<d<4$, up to next-to-leading order in a $1/N$
expansion. Our approach suggests an interesting duality property of the
critical $O(N)$ invariant theory. Also, solving our consistency relations we
obtain the next-to-leading order in $1/N$ correction for $C_{T}$ which
corresponds to the normalisation of the energy momentum tensor two-point
function.
