Theoretical and numerical analyses are presented of the passive coherent phasing of an array of fiber lasers that are combined in a single laser cavity by an N x1 coupler. In an initial linear analysis it is found that the brightness gain of the passive coherent array grows linearly for a small number of fibers, however, for practical parameters, the coherent brightness gain saturates at ~ 8 - 12 for large arrays. An intensity dependent index (Kerr) nonlinearity is then introduced and it is shown that the expected maximum improvement is modest, with the coherent brightness gain saturating at 10 - 14, depending on the strength of the nonlinearity. These results are compared with recent experiments.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.