  We investigate the statistical distribution of the zeros of Dirichlet
$L$--functions both analytically and numerically. Using the Hardy--Littlewood
conjecture about the distribution of prime numbers we show that the two--point
correlation function of these zeros coincides with that for eigenvalues of the
Gaussian unitary ensemble of random matrices, and that the distributions of
zeros of different $L$--functions are statistically independent. Applications
of these results to Epstein's zeta functions are shortly discussed.
