The development of fatigue damage in Co45Ni specimens during push—pull and reversed torsion tests, performed inside a scanning electron microscope, was observed and the different stress states compared. It appeared that transgranular crack initiation and development is delayed and intergranular crack initiation promoted under torsional loading. This was explained in terms of reduced surface distortion at the emergence of persistent slip bands (PSBs) and smaller compatibility stresses at the PSB‐matrix interfaces. The influence of the mechanical strength of grain boundaries on the difference between tensile and torsional fatigue lives is discussed.