  We analyze the low-$Q^2$ behavior of the axial form factor $G_A(Q^2)$, the
induced pseudoscalar form factor $G_P(Q^2)$, and the axial nucleon-to-$\Delta$
transition form factors $C^A_5(Q^2)$ and $C^A_6(Q^2)$. Building on the results
of chiral perturbation theory, we first discuss $G_A(Q^2)$ in a chiral
effective-Lagrangian model including the $a_1$ meson and determine the relevant
coupling parameters from a fit to experimental data. With this information, the
form factor $G_P(Q^2)$ can be predicted. For the determination of the
transition form factor $C^A_5(Q^2)$ we make use of an SU(6) spin-flavor
quark-model relation to fix two coupling constants such that only one free
parameter is left. Finally, the transition form factor $C^A_6(Q^2)$ can be
predicted in terms of $G_P(Q^2)$, the mean-square axial radius $\langle
r^2_A\rangle$, and the mean-square axial nucleon-to-$\Delta$ transition radius
$\langle r^2_{AN\Delta}\rangle$.
