We report on the expansion of a Fermi-Fermi mixture of Li-6 and K-40 atoms under conditions of strong interactions realized near the center of an interspecies Feshbach resonance. We observe two different phenomena of hydrodynamic behavior. The first one is the well-known inversion of the aspect ratio. The second one is a collective expansion, where both species stick together and despite of their different masses expand jointly. Our work constitutes a first step to explore the intriguing many-body physics of this novel system.