  We study the imaginary parts of the isoscalar electromagnetic and isovector
axial form factors of the nucleon close to the $3\pi$-threshold in covariant
baryon chiral perturbation theory. At the two-loop level, the contributions
arising from leading and next-to-leading order chiral $\pi N$-vertices, as well
as pion-induced excitations of virtual $\Delta(1232)$-isobars, are calculated.
It is found that the heavy baryon treatment overestimates substantially these
$3\pi$-continua. From a phenomenological analysis, that includes the narrow
$\omega(783)$-resonance or the broad $a_1$-resonance, one can recognize small
windows near threshold, where chiral $3\pi$-dynamics prevails. However, in the
case of the isoscalar electromagnetic form factors $G_{E,M}^s(t)$, the
radiative correction provided by the $\pi^0\gamma$-intermediate state turns out
to be of similar size.
