Actin is a multifunctional protein able to polymerise under ATP consumption as dynamic filaments involved in a number of membrane processes. Its ability to perform treadmilling motion is efficiently exploited to exert directed forces on the membrane structures where filaments are attached. In addition to the structural impact of fastening rigid actin filaments to a flexible membrane, out-of-equilibrium actin motions must impinge special membrane activity features. In this paper, we report an experimental study on the compression and shear rheology of lipid monolayers where filamentous actin is attached. Two different binding scenarios are proposed to simulate respectively sliding and sticking conditions. Covalent actin binding causes a significant enhancement of membrane fluidity, observed as a systematic decrease of compression and shear surface viscosities upon filament sticking. This fluidification can be only understood as a dynamical consequence of actin activity. These results constitute a first piece of rheological evidence on the active viscoelasticity of actin-based membranes.