The name Cyclorrhapha is used, in various modern classifications, to represent either a subgroup within the infraorder Muscomorpha, or simply a rankless group within the Brachycera. In either case, the Empidoidea are the sister taxon to the Cyclorrhapha. In the present classification, as the term Muscomorpha is used to refer to the sister taxon of the Empidoidea, the names "Muscomorpha" and "Cyclorrhapha" are effectively synonymous (though not entirely interchangeable: for nomenclatural purposes, it is always considered better if the endings of names of similar rank are consistent, and since all the other infraordinal names end in "-morpha", the use of "Cyclorrhapha" as an infraordinal name would be inconsistent).
In the Tree of Life Web Project, the name "Muscomorpha" refers to the Asilomorpha plus the Cyclorrhapha.