The fracture and fatigue crack growth behavior of two molybdenum alloys, containing 41 wt-% and 47.5 wt-% rhenium, respectively, are investigated. These alloys were provided in form of cold-wrought rods of 6 mm diameter and exhibit a refined microstructure with highly elongated grains and a strong fiber texture. Similarly processed pure molybdenum was used as reference material and exhibits a significantly coarser microstructure. SEN(T) and C(T) specimens were tested with R-L and L-R orientation. In both, quasi-static and fatigue crack growth experiments, L-R oriented cracks immediately kinked by 90° into the direction of grain elongation. This yields fracture toughness values and effective and long crack threshold values about twice as high as for R-L oriented cracks, which is in good agreement with calculations of a reduced local crack driving force. In both MoRe alloys a cyclic R-curve behavior was captured in fatigue crack growth tests at a load ratio of R = 0.1, while for MoRe47.5 it was still present at R = 0.7. This is attributed mainly to the coarser microstructure. The effective thresholds ∆Kth,eff of both MoRe alloys are remarkably low and deviate from a commonly used estimation, especially for the MoRe47.5 material. It is proposed that plasticity in these materials is facilitated by twinning, leading to the emission of partial dislocations from the crack tip. Although no clear microstructural or fractographic evidence was found, a recalculation of ∆Kth,eff considering partial dislocations indicates a good correlation with experimental values.