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 ǫ = 4 − d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in ǫ. 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. Typeset using REVTEX 1 I
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