  We introduce the notion of a relative pseudomonad, which generalises the
notion of a pseudomonad, and define the Kleisli bicategory associated to a
relative pseudomonad. We then present an efficient method to define pseudomonas
on the Kleisli bicategory of a relative pseudomonad. The results are applied to
define several pseudomonads on the bicategory of profunctors in an homogeneous
way, thus providing a uniform approach to the definition of bicategories that
are of interest in operad theory, mathematical logic, and theoretical computer
science.
