  We study the pion electromagnetic and $\gamma^* + \pi^0 \to \gamma$
transition form factors at intermediate momentum transfer. We calculate soft,
nonperturbative corrections to the leading perturbative amplitudes which arise
from the $q\bar q$-component of the pion wave function. We work in Minkowski
space and use a Lorentz covariant, gauge-invariant generalized perturbative
integral representation for the $q\bar q$ amplitudes. For the transition form
factor we find relative insensitivity to the detailed nonperturbative structure
of the wavefunction for $|q^2|\gsim 10$~GeV$^2$, whereas considerable
sensitivity is found for the electromagnetic form factor.
