  We study the operator product expansion in the AdS$_3$ WZNW model. The OPE of
primary fields and their spectral flow images is computed from the analytic
continuation of the expressions in the H$_3^+$ WZNW model, adding spectral
flow. We argue that the symmetries of the affine algebra require a truncation
which establishes the closure of the fusion rules on the Hilbert space of the
theory. Although the physical mechanism determining the decoupling is not
completely understood, we present several consistency checks on the results. A
preliminary analysis of factorization allows to obtain some properties of
four-point functions involving fields in generic sectors of the theory, to
verify that they agree with the spectral flow selection rules and to show that
the truncation must be realized in physical amplitudes for consistency.
