The double-orbit graph is a generalization of vertex transitive graphs, which contains many classic network models. Conditional edge-connectivity is an important index to measure the fault-tolerance and reliability of the networks. In this paper, we characterize the super-λ(2) double-orbit graphs with two orbits of the same size. Moreover, we give a sufficient condition for regular double-orbit graphs to be λ(3)-optimal, and characterize super-λ(3) regular double-orbit graphs