  Some exact relations for the spectral density $\rho(\lambda)$ of the
Euclidean Dirac operator in $QCD$ are derived. They follow directly from the
chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are
obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to
infinity and also in the theory defined in finite volume where the spectrum is
discrete and a nontrivial information on $\rho(\lambda)$ in the region $\lambda
\sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained.
These exact results should be confronted with "experimental" numerical
simulations on the lattices and in some particular models for $QCD$ vacuum
structure and may serve as a nontrivial test of the validity of these
simulations.
