Relativistic, fixed momentum-transfer dispersion relations are derived (but not proved) for pion scattering from $\ensuremath{\Sigma}$ and $\ensuremath{\Lambda}$ particles and the processes $\ensuremath{\pi}+\ensuremath{\Lambda}\ensuremath{\leftrightarrows}\ensuremath{\pi}+\ensuremath{\Sigma}$. Separate equations for the $S$- and $P$-wave amplitudes are obtained under the assumptions that high-energy processes and baryon recoil may be neglected. The $P$-wave equations are identical to those derived from Chew-Low theory for these processes. A brief discussion is given of the behavior of the $P$-wave amplitudes under the assumption of global symmetry. It is pointed out that the production of $K\ensuremath{-}N$ pairs may play an important role in both the $S$- and $P$-wave equations.