  We investigate the photon emission in pion-pion and pion-proton scattering in
the soft-photon limit where the photon energy $\omega \to 0$. The expansions of
the $\pi^{-} \pi^{0} \to \pi^{-} \pi^{0} \gamma$ and the $\pi^{\pm} p \to
\pi^{\pm} p \gamma$ amplitudes, satisfying the energy-momentum relations, to
the orders $\omega^{-1}$ and $\omega^{0}$ are derived. We show that these terms
can be expressed completely in terms of the on-shell amplitudes for $\pi^{-}
\pi^{0} \to \pi^{-} \pi^{0}$ and $\pi^{\pm} p \to \pi^{\pm} p$, respectively,
and their partial derivatives with respect to $s$ and $t$. The~structure term
which is non singular for $\omega \to 0$ is determined to the order
$\omega^{0}$ from the gauge-invariance constraint using the generalized Ward
identities for pions and the proton. For the reaction $\pi^{-} \pi^{0} \to
\pi^{-} \pi^{0} \gamma$ we discuss in detail the soft-photon theorems in the
versions of both F.E. Low and S. Weinberg. We show that these two versions are
different and must not be confounded. Weinberg's version gives the pole term of
a Laurent expansion in $\omega$ of the amplitude for $\pi^{-} \pi^{0} \to
\pi^{-} \pi^{0} \gamma$ around the phase-space point of zero radiation. Low's
version gives an approximate expression for the above amplitude at a fixed
phase-space point, corresponding to non-zero radiation. Clearly, the leading
and next-to-leading terms in theses two approaches must be, and are indeed,
different. We show their relation. We also discuss the expansions of
differential cross sections for $\pi^{-} \pi^{0} \to \pi^{-} \pi^{0} \gamma$
with respect to $\omega$ for $\omega \to 0$.
