Building on the superspace formulation for four-dimensional N = 2 matter-coupled supergravity developed in , we elaborate upon a general setting for field theory in N = 2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N = 2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W-0 is constant, W-0 = 1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N = 2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of N = 2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N = 2 -> N = 1 is performed for the action principle in general conformally flat N = 2 backgrounds, and examples of such reduction are given.