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At strong magnetic fields double-layer two-dimensional-electron-gas systemscan form an unusual broken symmetry state with spontaneous inter-layer phasecoherence. The system can be mapped to an equivalent system of pseudospin $1/2$particles with pseudospin-dependent interactions and easy-plane magnetic order.In this paper we discuss how the presence of a weak interlayer tunneling termalters the properties of double-layer systems when the broken symmetry ispresent. We use the energy functional and equations of motion derived earlierto evaluate the zero-temperature response functions of the double-layer systemand use our results to discuss analogies between this system andJosephson-coupled superconducting films. We also present a qualitative pictureof the low-energy charged excitations of this system. We show that parallelfields induce a highly collective phase transition to an incommensurate statewith broken translational symmetry.Comment: 26 pages, RevTex, 8 postscript figures (submitted to Phys. Rev. B

Spontaneous interlayer coherence in double-layer quantum Hall systems: Symmetry-breaking interactions, in-plane fields, and phase solitons