  Since the violent relaxation in hierarchical merging is incomplete,
elliptical galaxies retain a wealth of information about their formation
pathways in their present-day orbital structure. A variety of evidence
indicates that gas-rich major mergers play an important role in the formation
of elliptical galaxies. We simulate 1:1 disk mergers at seven different initial
gas fractions ranging from 0 to 40%, using the TreeSPH code Gadget-2. We
classify the stellar orbits in each remnant and construct radial profiles of
the orbital content, intrinsic shape, and orientation. The dissipationless
remnants are typically prolate-triaxial, dominated by box orbits within r_c ~
1.5Reff, and by tube orbits in their outer parts. As the gas fraction
increases, the box orbits within r_c are increasingly replaced by a population
of short axis tubes (z-tubes) with near zero net rotation, and the remnants
become progressively more oblate and round. The long axis tube (x-tube) orbits
are highly streaming and relatively insensitive to the gas fraction, implying
that their angular momentum is retained from the dynamically cold initial
conditions. Outside r_c, the orbital structure is essentially unchanged by the
gas. The 15-20% gas remnants often display disk-like kinematically distinct
cores (KDCs). These remnants show an interesting resemblance, in both their
velocity maps and intrinsic orbital structure, to the KDC galaxy NGC4365 (van
den Bosch et al. 2008). At 30-40% gas, the remnants are rapidly rotating, with
sharp embedded disks on ~ 1Reff scales. We predict a characteristic, physically
intuitive orbital structure for 1:1 disk merger remnants, with a distinct
transition between 1 and 3Reff that will be readily observable with combined
data from the 2D kinematics surveys SAURON and SMEAGOL.
