On coincidences of families of mappings on ordered sets

New results on fixed points and coincidences of families of set-valued mappings of partially ordered sets obtained without commutativity assumptions are presented. These results develop theorems on fixed points of an isotone self-mapping of an ordered set (for families of set-valued mappings) and theorems about coincidences of two set-valued mappings one of which is isotone and the other is covering (for finite families of set-valued mappings).