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Eigenchannel R-matrix calculations (including effects of long-range multipole interactions beyond the reaction volume) for Li– photodetachment partial cross sections from the vicinity of the Li 3s threshold to the Li 6s threshold (3.8 eV ≤ ħω ≤ 5.65 eV) are presented. Excellent agreement with recent relative total cross section measurements of U. Berzinsh et al. [Phys. Rev. Lett. 74, 4795 (1995)] in the vicinity of the Li 3s and Li 3p thresholds is found. The calculated resonance structures are analyzed in detail and compared with similar calculations for H– photodetachment above the H(n = 4) and H(n = 5) excited state thresholds. The non-hydrogenic Li+ core is shown to produce kinds of resonances in Li– photodetachment that are not observed in H– photodetachment.