  We present and apply a novel scheme for studying photon- and pion-nucleon
scattering beyond the threshold region. Partial-wave amplitudes for the
$\gamma\, N$ and $\pi N$ states are obtained by an analytic extrapolation of
subthreshold reaction amplitudes computed in chiral perturbation theory, where
the constraints set by electromagnetic-gauge invariance, causality and
unitarity are used to stabilize the extrapolation. Based on the chiral
Lagrangian we recover the empirical s- and p-wave amplitudes up to energies
$\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$.
