  We study theoretically the non-linear response properties of glass formers.
We establish several general results which, together with the assumption of
Time-Temperature Superposition, lead to a relation between the non-linear
response and the derivative of the linear response with respect to temperature.
Using results from Mode-Coupling Theory (MCT) and scaling arguments valid close
to the glass transition, we obtain the frequency and temperature dependence of
the non-linear response in the $\alpha$ and $\beta$-regimes. Our results
demonstrate that supercooled liquids are characterized by responses to external
perturbations that become increasingly non-linear as the glass transition is
approached. These results are extended to the case of inhomogeneous perturbing
fields.
