  In this paper we consider rough differential equations on a smooth manifold
$\left( M\right) .$ The main result of this paper gives sufficient conditions
on the driving vector-fields so that the rough ODE's have global (in time)
solutions. The sufficient conditions involve the existence of a complete
Riemannian metric $\left( g\right) $ on $M$ such that the covariant derivatives
of the driving fields and their commutators to a certain order (depending on
the roughness of the driving path) are bounded. Many of the results of this
paper are generalizations to manifolds of the fundamental results in
\cite{Bailleul2015a}.
