  The weak localization (WL) contribution to the two-level correlation function
is calculated for two-dimensional disordered conductors. Our analysis extends
to the nondiffusive (ballistic) regime, where the elastic mean path is of order
of the size of the system. In this regime the structure factor (the Fourier
transform of the two-point correlator) exhibits a singular behavior consisting
of dips superimposed on a smooth positive background. The strongest dips appear
at periods of the periodic orbits of the underlying clean system. Somewhat
weaker singularities appear at times which are sums of periods of two such
orbits. The results elucidate various aspects of the weak localization physics
of ballistic chaotic systems.
