There now exists a wealth of experimental evidence that Sr2RuO4 is an odd-p
arity superconductor. Experiments further indicate that among the bands ste
mming from the Ru {xy,xz,yz} orbitals, the portion of the Fermi surface ari
sing from the xy orbitals exhibits a much larger gap than the portions of t
he Fermi surface arising from the {xz,yz} orbitals. In this paper the role
of impurities in such an orbital-dependent superconducting state is examine
d within the Born approximation. In contrast to expected results for a node
less p-wave superconductor, the unique nature of the superconducting state
in Sr2RuO4 implies that a low concentration of impurities strongly influenc
es the low-temperature behavior.