The spectra of thin slabs of single‐crystal MnF2and KMnF3at low temperatures have been measured, both in the far infrared (40–360 cm−1) and in the visible (3850–4000 Å). The far infrared spectra consist of many sharp lines superimposed on a broad phonon background. The sharp lines are caused by processes involving the simultaneous creation of as many as 8 magnons, sometimes accompanied by the creation or absorption of standing elastic waves. In the visible spectrum, exciton lines with magnon sidebands are observed, accompanied by many weak satellite lines. The satellite lines correspond to processes in which as many as 30 magnons may be created simultaneously. For both substances, the observed lines in both spectra can be fitted to within experimental accuracy using combinations of only 3 single‐magnon energies.