  We calculate the $O(p^6)$ corrections to the anomalous form factors appearing
in $\pi^+$, $K^+ \to e^+ \nu \gamma,\ \mu^+\nu\gamma$ and $K_{l4}$ decays in
Chiral Perturbation Theory. The relevant dimension $6$ terms of the lagrangian
are evaluated assuming their saturation by the vector meson contribution.
