The paper deals with intrinsic behaviour of long fatigue cracks under the remote mode II and mode III loading, particularly with the intrinsic (effective) thresholds and the crack path geometry from the point of view of the competition between the local shear and the local opening growth mode. Unlike in the case of opening mode I cracks, the microstructure can significantly influence the dominant growth mechanism of the shear-mode cracks in dependence of the type of the secondary phase. The cementite lamellae of the pearlitic steel change the local growth mode from mode II to mode I and increased the effective mode II and mode III thresholds, whereas the β-Ti lamellae of the Ti6Al4V alloy do not change the intrinsic behaviour. The difference can be explained by different ability of dislocations to cross the phase boundary. The competition between the local shear and the local opening growth modes in metals is assessed by a newly proposed mode I branching criterion based on fracture mechanics. Using this criterion, the value of the deflection angle corresponding to the transition between the dominant mode I and dominant mode II crack growth was found to be of 46 •. This result agrees well with the previously published value of the transient angle based on identification of characteristic fractographical patterns on the fracture surfaces of investigated metallic materials.