Modelling as well as simulation of materials behaving both brittle and/or ductile in connection with anisotropic damage is still a challenging task, especially in the case of finite deformations. This has already been intensively discussed in our recently published work of Reese et al. [1], which, however, uses a different kinematic approach than the one that will be presented here. In addition to the formulation of a constitutive law, a mesh-independent formulation in the presence of large deformations is essential from a computational point of view. Therefore, in the presented work, both a thermodynamically consistent elasto-damage-plasticity material formulation and its gradientextension -based on the invariants of the damage tensor -are discussed, which can be understood as a micromorphic extension following Forest [2]. Thus, although a second order damage tensor is used, only three additional (micromorphic) fields are required to account for the nonlocal nature of damage. Choosing damage itself for the gradient-extension is of course not a unique choice, however, the very good experience of our research group following this approach for different kinds of inelastic and anisotropic material effects (see e.g. [3,4]) motivates this choice.