  We study non-abelian systems of Painlev\'e type. To derive them, we introduce
an auxiliary autonomous system with the frozen independent variable and
postulate its integrability in the sense of the existence of a non-abelian
first integral that generalizes the Okamoto Hamiltonian. All non-abelian
P6-P2-systems with such integrals are found. A coalescence limiting scheme is
constructed for these non-abelian Painlev\'e systems. This allows us to
construct an isomonodromic Lax pair for each of them.
