We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-col
or QCD at nonzero baryon density when the eigenvalues become complex. The q
uasi-zero modes and their role for chiral symmetry breaking and the deconfi
nement transition are examined. The bulk of the spectrum and its relation t
o quantum chaos is considered. A comparison with predictions from random ma
trix theory is presented. An analogous analysis is performed for the spectr
um of the Gor'kov representation of the fermionic action.