  In this paper we give, for the first time, a qualitative description of the
asymptotic dynamics of a class of non-tilted spatially homogeneous (SH)
cosmologies, the so-called exceptional Bianchi cosmologies, which are of
Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly,
it is generic within the class of non-tilted SH cosmologies, being of the same
generality as the models of Bianchi types VIII and IX. Secondly, it is the SH
limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies.
  Using the orthonormal frame formalism and Hubble-normalized variables, we
show that the exceptional Bianchi cosmologies differ from the non-exceptional
Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the
models exhibit an oscillatory approach to the initial singularity and hence are
not asymptotically self-similar. Secondly, at late times, although the models
are asymptotically self-similar, the future attractor for the vacuum-dominated
models is the so-called Robinson-Trautman SH model instead of the vacuum SH
plane wave models.
