  For a covariant functor W. Fulton and R. MacPherson defined \emph{an
operational bivariant theory} associated to this covariant functor. In this
paper we will show that given a contravariant functor one can similarly
construct a ``dual" version of an operational bivariant theory, which we call a
\emph{co-operational} bivariant theory. If a given contravariant functor is the
usual cohomology theory, then our co-operational bivariant group for the
identity map consists of what are usually called ``cohomology operations". In
this sense, our co-operational bivariant theory consists of
\emph{``generalized"} cohomology operations.
