  We study the off-equilibrium two-point critical response and correlation
functions for the relaxational dynamics with a coupling to a conserved density
(Model C) of the O(N) vector model. They are determined in an \epsilon=4-d
expansion for vanishing momentum. We briefly discuss their scaling behaviors
and the associated scaling forms are determined up to first order in epsilon.
The corresponding fluctuation-dissipation ratio has a non trivial large time
limit in the aging regime and, up to one-loop order, it is the same as that of
the Model A for the physically relevant case N=1. The comparison with
predictions of local scale invariance is also discussed.
