  We show how to assign initial data for the characteristic
Einstein-Yang-Mills-Higgs system on two intersecting smooth null hypersurfaces.
We successfully adapt the hierarchical method set up by A. D. Rendall to solve
the same problem for the Einstein equations in vacuum and with perfect fluid
source. Unlike the work of Rendall, many delicate calculations and expressions
are given in details so as to address, in a forthcoming work, the issue of
global resolution of the characteristic initial value problem for the
Einstein-Yang-Mills-Higgs system. The method obviously applies to the
Einstein-Maxwell and the Einstein-scalar field models.
