A hypothesis is presented for fatigue failure of concrete structures. It is based on a deformation formulation, and utilizes the monotonic F - delta curve and the fatigue creep curve. The hypothesis is applied to flexural fatigue tests on notched beams of a plain high performance concrete. The experimental part comprises monotonic loading in deformation control and constant amplitude loading at three different load levels in flexural tension. The hypothesis is in all essentials consistent with the experimental findings. Furthermore, it provides a deformation formulation for accumulated damage estimation and remaining service life prediction, which takes account for the nonlinear nature of damage development in contrast to the linear Palmgren-Miner hypothesis