  We analyze in detail three classes of isomondromy deformation problems
associated with integrable systems. The first two are related to the scaling
invariance of the $n\times n$ AKNS hierarchies and the Gel'fand-Dikii
hierarchies. The third arises in string theory as the representation of the
Heisenberg group by $[(L^{k/n})_+,L]=I$ where $L$ is an $n^{th}$ order scalar
differential operator. The monodromy data is constructed in each case; the
inverse monodromy problem is solved as a Riemann-Hilbert problem; and a simple
proof of the Painlev\'e property is given for the general case
