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Ni K-edge x-ray-absorption spectroscopy ͑XAS͒ measurements on a series of perovskite-layer-based nickelate compounds, with varying formal Ni valence, are presented. Spectral features that vary systematically with the Ni configuration are identified for these Ruddlesden-Popper phase and Sr substituted Ln 2Ϫx Sr x NiO 4 ͑LnϭLa and Nd͒ materials. Selected polarized XAS results on the La 2Ϫx Sr x NiO 4 system emphasize that a collapse of the Ni 4p -4p energy separation accompanies the substantial contraction of the apical Ni-O bond length in this series. In view of this, it is suggested that a displacement of the apical oxygen ͑O ab ͒ could play an important role in the small polarons previously proposed to form in this system. The polarized XAS results also provide evidence for in-plane character for the Ni-site component of the doped holes in this system. The XAS evidence supporting an increasing Ni d 7 ground-state admixture in these materials, with increasing formal Ni valence, is discussed. This discussion is couched in terms of simplified Ni d configuration modeling, which emphasizes the close energetic proximity of the Ni d 8 state to O p states in these systems.