  Yang-Mills models with compact gauge group coupled to matter fields are
considered. The general tools developed in a companion paper are applied to
compute the local cohomology of the BRST differential $s$ modulo the exterior
spacetime derivative $d$ for all values of the ghost number, in the space of
polynomials in the fields, the ghosts, the antifields (=sources for the BRST
variations) and their derivatives. New solutions to the consistency conditions
$sa+db=0$ depending non trivially on the antifields are exhibited. For a
semi-simple gauge group, however, these new solutions arise only at ghost
number two or higher. Thus at ghost number zero or one, the inclusion of the
antifields does not bring in new solutions to the consistency condition
$sa+db=0$ besides the already known ones. The analysis does not use power
counting and is purely cohomological. It can be easily extended to more general
actions containing higher derivatives of the curvature, or Chern-Simons terms.
