  We review the canonical superenergy tensor and the canonical angular
supermomentum tensors in general relativity and calculate them for space-time
homogeneous G\"odel universes to show that both of these tensors do not, in
general, vanish. We consider both an original dust-filled pressureless acausal
G\"odel model of 1949 and a scalar-field-filled causal G\"odel model of Rebou\c
cas and Tiomno. For the acausal model, the non-vanishing components of
superenergy of matter are different from those of gravitation. The angular
supermomentum tensors of matter and gravitation do not vanish either which
simply reflects the fact that G\"odel universe rotates. However, the axial
(totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It
is interesting that superenergetic quantities are {\it sensitive} to causality
in a way that superenergy density $_g S_{00}$ of gravitation in the acausal
model is {\it positive}, while superenergy density $_g S_{00}$ in the causal
model is {\it negative}. That means superenergetic quantities might serve as
criterion of causality in cosmology and prove useful.
