  String-inspired 1+1-dimensional gravity is coupled to Yang-Mills fields in
the Cangemi-Jackiw gauge-theoretical formulation, based on the extended
Poincar\'e group. A family of couplings, which involves metrics obtainable from
the physical metric with a conformal rescaling, is considered, and the
resulting family of models is investigated both at the classical and the
quantum level. In particular, also using a series of Kirillov-Kostant phases,
the wave functionals that solve the constraints are identified.
