  This paper revisits the concept of rough paths of inhomogeneous degree of
smoothness (geometric \Pi-rough paths in our terminology) sketched by Lyons
("Differential equations driven by rough signals", Revista Mathematica Iber.
Vol 14, Nr. 2,215-310, 1998). Although geometric \Pi-rough paths can be treated
as p-rough paths for a sufficiently large p and the theory of integration of
Lip-\gamma one-forms (\gamma>p-1) along geometric p-rough paths applies, we
prove the existence of integrals of one-forms under weaker conditions.
Moreover, we consider differential equations driven by geometric \Pi-rough
paths and give sufficient conditions for existence and uniqueness of solution.
