  Bianchi type I and type IX ('Mixmaster') geometries are investigated within
the framework of Ho\v{r}ava-Witten cosmology. We consider the models for which
the fifth coordinate is a $S^1/Z_2$ orbifold while the four coordinates are
such that the 3-space is homogeneous and has geometry of Bianchi type I or IX
while the rest six dimensions have already been compactified on a Calabi-Yau
space. In particular, we study Kasner-type solutions of the Bianchi I field
equations and discuss Kasner asymptotics of Bianchi IX field equations. We are
able to recover the isotropic 3-space solutions found by Lukas {\it et al}.
Finally, we discuss if such Bianchi IX configuration can result in chaotic
behaviour of these Ho\v{r}ava-Witten cosmologies.
