  The detection of a time variation of the angle between two distant sources
would reveal an anisotropic expansion of the Universe. We study this effect of
"cosmic parallax" within the "ellipsoidal universe" model, namely a particular
homogeneous anisotropic cosmological model of Bianchi type I, whose attractive
feature is the potentiality to account for the observed lack of power of the
large-scale cosmic microwave background anisotropy. The preferred direction in
the sky, singled out by the axis of symmetry inherent to planar symmetry of
ellipsoidal universe, could in principle be constrained by future cosmic
parallax data. However, that will be a real possibility if and when the
experimental accuracy will be enhanced at least by two orders of magnitude.
