In this article, it is shown that every flock of a hyperbolic quadric
and every flock of
a quadratic cone
in
, for
a field, is in a transitive
parallelism of
or
,
respectively. Furthermore, it is shown it is possible to have parallelisms of
quadratic cones by maximal partial flocks. The theory of parallelisms of
quadratic cones is generalized to analogous results for parallelisms of
-cones.
