  We present first-principles studies on the orbital states of the layered
perovskites Ca$_{2-x}$Sr$_x$RuO$_4$. The crossover from antiferromagnetic (AF)
Mott insulator for $x < 0.2$ to nearly ferromagnetic (FM) metal at $x=0.5$ is
characterized by the systematic change of the $xy$ orbital occupation. For the
AF side ($x < 0.2$), we present firm evidence for the $xy$ ferro-orbital
ordering. It is found that the degeneracy of $t_{2g}$ (or $e_g$) states is
lifted robustly due to the two-dimensional (2D) crystal-structure, even without
the Jahn-Teller distortion of RuO$_6$. This effect dominates, and the
cooperative occupation of $xy$ orbital is concluded. In contrast to recent
proposals, the resulting electronic structure explains well both the observed
X-ray absorption spectra and the double peak structure of optical conductivity.
For the FM side ($x=0.5$), however, the $xy$ orbital with half filling opens a
pseudo-gap in the FM state and contributes to the spin $S$=1/2 moment (rather
than $S$=1 for $x$=0.0 case) dominantly, while $yz,zx$ states are itinerant
with very small spin polarization, explaining the recent neutron data
consistently.
