  We consider off-equilibrium dynamics at the critical temperature in a class
of glassy system. The off-equilibrium correlation and response functions obey a
precise scaling form in the aging regime. The structure of the {\it
equilibrium} replicated Gibbs free energy fixes the corresponding {\it
off-equilibrium} scaling functions implicitly through two functional equations.
The details of the model enter these equations only through the ratio $w_2/w_1$
of the cubic coefficients (proper vertexes) of the replicated Gibbs free
energy. Therefore the off-equilibrium dynamical exponents are controlled by the
very same parameter exponent $\lambda=w_2/w_1$ that determines equilibrium
dynamics. We find approximate solutions to the equations and validate the
theory by means of analytical computations and numerical simulations.
