AbstractIn this work, collisionless Landau fluid models are combined with collisional fluid models using a Padé approximation that is accurate in both collisionality limits. The collisionless models capture Landau damping through a nonlocal integro‐differential sub‐diffusion operator with ballistic characteristics. Collisional extensions of Landau fluid models are derived by analyzing the higher order moment equations which combine a Landau closure with collisional friction forces. The model derived here evolves fluid moments for density, parallel velocity, and anisotropic pressure and includes the frictional heat flux, the parallel thermal force and anisotropic electrical conductivity. Since anisotropies must vanish in the collisional limit, a simple closure can be derived if the friction force neglects pitch‐angle scattering for the closure moments themselves. The resulting plasma physics model is potentially quite useful for applications in magnetic fusion and astrophysics. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)