Three new species of Geoplana Stimpson, 1857 from south Brazil, Geoplana ficki sp. nov., G. carbayoi sp. nov., and G. baptistae sp. nov., with dark, nearly homogeneous dorsum, reddish or orange venter, and eyes spreading over the dorsum, are described. The three can be included in the Graff group of “large, broad and flat species”, designated the G. applanatagroup by C. G. Froehlich (1967). The first described species presenting this pattern was G. rufiventris Schultze & Müller, 1857. Later, several other authors described various species exhibiting the “dark dorsal surface and orange or reddish ventral side” pattern. These species constitute an assemblage which will be here designated the G. rufiventris-complex. Apart from presenting a similar pattern, a further considerable difficulty in differentiating these taxa from the other large, broad and flat species of the genus Geoplana which were included in Froehlich’s original G. applanata-group, resides in their possessing a very homogeneous copulatory apparatus. Characteristics of their external and internal morphology are here discussed to simplify the differentiation of sub-groups and comparison of species.