  We develop Chiral Perturbation Theory for chirally broken theories with
fermions in two different representations of the gauge group. Any such theory
has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional
Nambu-Goldstone boson when spontaneously broken. We calculate the
next-to-leading order corrections for the pseudoscalar masses and decay
constants, which include the singlet Nambu-Goldstone boson, as well as for the
two condensates. The results can be generalized to more than two
representations.
