  Based on the Ginzburg-Landau functional of E_{u} symmetry presented by
Agterberg, vortex states of Sr_{2}RuO_{4} are studied in detail over
$H_{c1}\lesssim H \leq H_{c2}$ by using the Landau-level expansion method. For
the field in the basal plane, it is found that (i) the second superconducting
transition should be present irrespective of the field direction; (ii) below
this transition, a characteristic double-peak structure may develop in the
magnetic-field distribution; (iii) a third transition may occur between two
different vortex states. It is also found that, when the field is along the c
axis, the square vortex lattice may deform through a second-order transition
into a rectangular one as the field is lowered from H_{c2}. These predictions
will be helpful in establishing the E_{u} model for Sr_{2}RuO_{4}.
