  The method of solution of the initial value constraints for pure canonical
gravity in terms of Ashtekar's new canonical variables due to CDJ is further
developed in the present paper. There are 2 new main results : 1) We extend the
method of CDJ to arbitrary matter-coupling again for non-degenerate metrics :
the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part
when solving the vector constraint and that the Klein-Gordon-field is used,
instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar
constraint. 2) The 2nd result is that one can solve the general initial value
constraints for arbitrary matter coupling by a method which is completely
independent of that of CDJ. It is shown how the Yang-Mills and gravitational
Gauss constraints can be solved explicitely for the corresponding electric
fields. The rest of the constraints can then be satisfied by using either
scalar or spinor field momenta. This new trick might be of interest also for
Yang-Mills theories on curved backgrounds.
