  Earlier work showed that the track in the X-ray hardness-intensity diagram of
Cir X-1 corresponds to a Z track in its color-color diagram. In this paper, we
study the cross spectrum of Cir X-1 in different regions of the
hardness-intensity diagram with $RXTE$/PCA data. Comparing the light curves of
Cir X-1 for the energy band 1.8-5.1 keV to those for 5.1-13.1 keV, we find that
Cir X-1 exhibits a hard time lag on the horizontal branch, and a soft time lag
on both the normal and the flaring branch. This indicates that Cir X-1 is
similar to GX 5-1 and Cyg X-2 on the horizontal branch, but is different from
them on the normal branch. We briefly discuss the mechanism of the time lags in
the context of Comptonization models.
