  We consider a smooth semiflow strongly focusing monotone with respect to a
cone of rank k on a Banach space. We obtain its generic dynamics, that is,
semiorbits with initial data from an open and dense subset of any bounded open
set are either pseudo-ordered or convergent to an equilibrium. For the case
k=1, it is the celebrated Hirsch's Generic Convergence Theorem. For the case
k=2, we obtain the generic Poincare-Bendixson Theorem.
