The comultiplication formula for fusion products of untwisted represen
tations of the chiral algebra is generalized to include arbitrary twis
ted representations. We show that the formulae define a tensor product
with suitable properties, and determine the analogue of Zhu's algebra
for arbitrary twisted representations. As an example we study the fus
ion of representations of the Ramond sector of the N = 1 and N = 2 sup
erconformal algebra. In the latter case, certain subtleties arise whic
h we describe in detail.