Two inner channels in the southern branch of Kasei Valles are among the best preserved examples of fluvial erosion on Mars. Attributes of the channels include arcuate alcoves, perched boulders, and a concave-up longitudinal profile, all of which are consistent with the interpretation that these channels were carved by a Newtonian fluid. The sharp concavity of the longitudinal profile is comparable to a terrestrial alluvial system with a minimum work profile. The shape of the profile suggests that the system was in a quasi-equilibrium state but was not active long enough to achieve grade. Associated with these channels is a platy meter-scale texture, identified in high-resolution Mars Orbiter Camera images. Although a lava flow could explain many of the material properties of the platy surface texture, we speculate that this texture in the immediate proximity to the southern Kasei Valles inner channels may be related to waning floodwaters moving through the inner channels and is a mudflow deposit.