New single‐site catalysts based on mixed‐linker metal‐organic frameworks with DUT‐5 structure, which contain immobilized Co2+, Mn2+ and Mn3+ complexes, have successfully been synthesized via post‐synthetic modification. 2,2’‐Bipyridine‐5,5’‐dicarboxylate linkers were directly metalated, while 2‐amino‐4,4’‐biphenyldicarboxylate linkers were post‐synthetically modified by their conversion to Schiff‐base ligands and a subsequent immobilization of the metal complexes. The resulting materials were used as catalysts in the selective epoxidation of trans‐stilbene and the activities and selectivities of the different catalysts were compared. The influence of various reaction parameters on conversion, yield and selectivity were investigated. Very low catalyst amounts of 0.02 mol % were sufficient to obtain a high conversion of trans‐stilbene using molecular oxygen from air as the oxidant. For cobalt‐containing MOF catalysts, conversions up to 90 % were observed and, thus, they were more active than their manganese‐containing counterparts. Recycling experiments and hot filtration tests proved that the reactions were mainly catalyzed via heterogeneous pathways.