  In this paper, we study the asymptotic relation between the first crossing
point and the last exit time for Gaussian order statistics which are generated
by stationary weakly and strongly dependent Gaussian sequences. It is shown
that the first crossing point and the last exit time are asymptotically
independent and dependent for weakly and strongly dependent respectively. The
asymptotic relation between the first exit time and the last exit time for
stationary weakly and strongly dependent Gaussian Gaussian sequences are also
obtained.
