Ferromagnetic alloys of manganese and tin have been used to obtain large internal magnetic fields at the tin nuclei. The resultant Zeeman splittings of the two low levels of Sn119 have been measured by observing the hyperfine spectra in the resonant absorption of the 24-kev radiation of Sn119. In Mn4Sn an internal field of roughly 40 koe was found. In this field the splitting of the ground state was observed but that of the excited state was unresolved. In Mn2Sn an internal field of about 190 koe was produced. In this field additional structure was obtained which was attributed to the splitting of the excited state. The measured splitting gives a value of (0.78+/-0.08) nm for the magnetic moment of the excited state.