  We characterise simply-connected biquotients which potentially admit metrics
of holonomy G_2. We prove that there are at most three real homotopy types of
rationally elliptic such manifolds---all of them being formal. In the course of
this examination we classify rationally elliptic homotopy types and
characterise 7-dimensional simply-connected biquotients from a rational point
of view. Moreover, we also investigate further manifolds of special holonomy,
like manifolds of holonomy Spin(7) or Sp(n)\Sp(1) in special situations
provided by rational ellipticity or geometric formality.
