We report the discovery of two new dwarf galaxies, Lacerta I/Andromeda XXXI (Lac I/And XXXI) and Cassiopeia III/Andromeda XXXII (Cas III/And XXXII), in stacked Pan-STARRS1 r P1- and i P1-band imaging data. Both are luminous systems (MV ~ –12) located at projected distances of 20fdg3 and 10fdg5 from M31. Lac I and Cas III are likely satellites of the Andromeda galaxy with heliocentric distances of 756−28+44kpc and 772−56+61kpc, respectively, and corresponding M31-centric distances of 275 ± 7 kpc and 144−4+6kpc. The brightest of recent Local Group member discoveries, these two new dwarf galaxies owe their late discovery to their large sizes (rh=4.2−0.5+0.4 arcmin or 912−93+124pc for Lac I; rh=6.5−1.0+1.2 arcmin or 1456 ± 267 pc for Cas III) and consequently low surface brightness (μ0 ~ 26.0 mag arcsec–2), as well as to the lack of a systematic survey of regions at large radii from M31, close to the Galactic plane. This latter limitation is now alleviated by the 3π Pan-STARRS1 survey, which could lead to the discovery of other distant Andromeda satellite dwarf galaxies.Astronom