Ottosen, Stenström and Ristinmaa proposed in 2008 a continuum based high-cycle
fatigue (HCF) model which is inherently multiaxial and offers several advantages in comparison
to classical multiaxial fatigue models. The key ingredients of such model are construction of a
moving endurance function and the evolution equations describing the movement and damage
evolution. This format is quite general, inherently multiaxial and is not based on heuristic cycle-
counting approaches. In this talk we discuss extensions of the basic isotropic HCF model to
anisotropy and low-cycle fatigue. Different forms to construct the endurance function are given,
e.g. how to better capture the mean stress behaviour (Haigh-diagram). This is archieved by
using the solution of diffusion-reaction equation. Based on the famous Murakami equation, which
describes how fatigue strength depends on defect size, we also discuss how the influence of defect
size on the endurance function can be taken into account. Coarsening from micromechanical
crystal plasticity models is also discussed.