Images have been obtained at the 6-m telescope at the Special Astrophysical Observatory ( SAO ) of the Russian Academy of Sciences in the H \alpha line and in the continuum for 20 dwarf spheroidal satellites of M31 : And XI-And XXX , plus the distant Globular cluster Bol 520 . Their star formation rates ( FR ) are estimated using the H \alpha flux and the ultraviolet FUV flux measured with the GALEX space telescope . Most of the dSph satellites of M31 have extremely low star formation rates with a characteristic upper limit of SFR \sim 5 \times 10 ^ { -7 } . We have made similar estimates of SFR from the H \alpha and FUV fluxes for 13 galaxies with low surface brightness recently discovered in the neighborhood of M81 . Eleven of them are physical satellites of M81 with typical SFR < 5 \times 10 ^ { -5 } . The median stellar masses of these satellites of M31 and M81 are 0.9 and 1.9 million solar masses , respectively . Our H \alpha observations place a 2–3 times stricter limit on the value of SFR than the data from the GALEX satellite , with a substantially higher ( 3–5 times ) angular resolution .