The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads
are described. More specifically, a notion of a {\em Morita context} comprising
of two monads, two bialgebra functors and two connecting maps is introduced. It
is shown that in many cases equivalences between categories of algebras are
induced by such Morita contexts. The Eilenberg-Moore category of
representations of a Morita context is constructed. This construction allows
one to associate two pairs of adjoint functors with right adjoint functors
having a common domain or a {\em double adjunction} to a Morita context. It is
shown that, conversely, every Morita context arises from a double adjunction.
The comparison functor between the domain of right adjoint functors in a double
adjunction and the Eilenberg-Moore category of the associated Morita context is
defined. The sufficient and necessary conditions for this comparison functor to
be an equivalence (or for the {\em moritability} of a pair of functors with a
common domain) are derived.