  We consider the topological dynamics of closed relations(CR) by studying one
of the oldest dynamical property - `transitivity'. We investigate the two kinds
of (closed relation) CR-dynamical systems - $(X,G)$ where the relation $G
\subseteq X \times X$ is closed and $(X,G, \bullet)$ giving the `suitable
dynamics' for a suitable closed relation $G$, where $X$ is assumed to be a
compact metric space without isolated points.
  $(X,G)$ gives a general approach to study initial value problems for a set of
initial conditions, whereas $(X,G, \bullet)$ gives a general approach to study
the dynamics of both continuous and quasi-continuous maps.
  We observe that the dynamics of closed relations is richer than the dynamics
of maps and find that we have much more versions of transitivity for these
closed relations than what is known for maps.
