  In the theory of disordered systems the spectral form factor $S(\tau)$, the
Fourier transform of the two-level correlation function with respect to the
difference of energies, is linear for $\tau<\tau_c$ and constant for
$\tau>\tau_c$. Near zero and near $\tau_c$ its exhibits oscillations which have
been discussed in several recent papers. In the problems of mesoscopic
fluctuations and quantum chaos a comparison is often made with random matrix
theory. It turns out that, even in the simplest Gaussian unitary ensemble,
these oscilllations have not yet been studied there. For random matrices, the
two-level correlation function $\rho(\lambda_1,\lambda_2)$ exhibits several
well-known universal properties in the large N limit. Its Fourier transform is
linear as a consequence of the short distance universality of
$\rho(\lambda_1,\lambda_2)$. However the cross-over near zero and $\tau_c$
requires to study these correlations for finite N. For this purpose we use an
exact contour-integral representation of the two-level correlation function
which allows us to characterize these cross-over oscillatory properties. The
method is also extended to the time-dependent case.

Condensed Matter