  A method is presented for solving the characteristic initial value problem
for the collision and subsequent nonlinear interaction of plane gravitational
or gravitational and electromagnetic waves in a Minkowski background. This
method generalizes the monodromy transform approach to fields with nonanalytic
behaviour on the characteristics inherent to waves with distinct wave fronts.
The crux of the method is in a reformulation of the main nonlinear symmetry
reduced field equations as linear integral equations whose solutions are
determined by generalized (``dynamical'') monodromy data which evolve from data
specified on the initial characteristics (the wavefronts).
