  The microstructural characteristics of a single crystalline nickel based
superalloy (AM1) tested under high temperature fatigue at 950$^\circ$C are
reported. For repeated fatigue (R$_\varepsilon$=0) through a range of cycle
numbers N with imposed total strain amplitude $\Delta\varepsilon^t$, two main
types of behaviour are found depending on N and $\Delta\varepsilon^t$. This
allows a map of microstructures versus the number of cycles N and
$\Delta\varepsilon^t$ to be constructed. A domain called A presents anisotropic
microstructures due either to a partition of the plasticity throughout the k
channels, or to an oriented coarsening of the k% precipitates of the so-called
type N (rafts perpendicular to the loading axis). The domain called H shows
homogeneous deformation microstructures. The coarsening observed in repeated
fatigue is accounted for on the basis of a model proposed earlier in the
literature by V\'eron. Alternate fatigue (R$_\varepsilon$ = -1) also leads to
the same type of coarsening, even for a very low number of cycles (N=113). The
microstructures observed are ascribed to internal stress effects and are
related to the possible shearing of the precipitates and to different diffusion
processes.
