The interplay between the superconducting gap and normal-state pseudogap in the bilayer cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. It is shown that the charge carrier interaction directly from the interlayer coherent hopping in the kinetic energy by exchanging spin excitations does not provide the contribution to the normal-state pseudogap in the particle-hole channel and superconducting gap in the particle-particle channel, while only the charge carrier interaction directly from the intralayer hopping in the kinetic energy by exchanging spin excitations induces the normal-state pseudogap in the particle-hole channel and superconducting gap in the particle-particle channel, and then the two-gap behavior is a universal feature for the single layer and bilayer cuprate superconductors.
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