  We study the spectrum of the QCD Dirac operator for two colors with fermions
in the fundamental representation and for two or more colors with adjoint
fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is
spontaneously broken according to $SU(2N_f)\to Sp(2N_f)$ and $SU(N_f)\to
O(N_f)$, respectively, rather than the symmetry breaking pattern $SU(N_f)
\times SU(N_f) \to SU(N_f)$ for QCD with three or more colors and fundamental
fermions. In this paper we study the Dirac spectrum for the first two symmetry
breaking patterns. Following previous work for the third case we find the Dirac
spectrum in the domain $\lambda \ll \Lambda_{\rm QCD}$ by means of partially
quenched chiral perturbation theory. In particular, this result allows us to
calculate the slope of the Dirac spectrum at $\lambda = 0$. We also show that
for $\lambda \ll 1/L^2 \Lambda_{QCD}$ (with $L$ the linear size of the system)
the Dirac spectrum is given by a chiral Random Matrix Theory with the
symmetries of the Dirac operator.
