  We provide a new algebraic description of the structure on the set of all
unstable cohomology operations for a suitable generalised cohomology theory,
E^*. Our description is as a graded and completed version of a Tall-Wraith
monoid. The E^*-cohomology of a space X is a module for this Tall-Wraith
monoid. We also show that the corresponding Hopf ring of unstable co-operations
is a module for the Tall-Wraith monoid of unstable operations. Further examples
are provided by considering operations from one theory to another.
