  In this talk we study beyond Standard Model scenarios where the Higgs is
non-linearly realized. The one-loop ultraviolet divergences of the low-energy
effective theory at next-to-leading order, O(p^4), are computed by means of the
background-field method and the heat-kernel expansion. The power counting in
non-linear theories shows that these divergences are determined by the
leading-order effective Lagrangian L_2. We focus our attention on the most
important O(p^4) divergences, which are provided by the loops of Higgs and
electroweak Goldstones, as these particle are the only ones that couple through
derivatives in L_2. The one-loop divergences are renormalized by O(p^4)
effective operators, and set their running. This implies the presence of chiral
logarithms in the amplitudes along with the O(p^4) low-energy couplings, which
are of a similar importance and should not be neglected in next-to-leading
order effective theory calculations, e.g. in composite scenarios.
