Diverse new basal (aschizan) Cyclorrhapha fossilized in amber are described from the Tertiary and Cretaceous, and their relationships are examined with character-based phylogenetic hypotheses for each family or family group. There are 18 new species in 15 genera (11 of them new) and four families plus the Syrphoidea. Fossils are from the Early Cretaceous of Lebanon, Late Cretaceous of New Jersey (United States) and Alberta (Canada), Eocene of the eastern Baltic coast, and Miocene of the Dominican Republic, but predominantly from the mid-Cretaceous of Myanmar. Stem-group Lonchopteroidea are Alonchoptera lebanica, n. gen., n.sp., and Lonchopterites burmensis, n. sp. Platypezidae include the stem groups Burmapeza radicis, n. gen., n. sp., Canadopeza biacrosticha, n. gen., n. sp., and Calvopeza divergens, n. gen., n. sp. An unnamed Microsania sp. is the first definitive Platypezidae in Baltic amber; Lebanopeza azari, n. gen., n. sp., is a stem group to the Microsaniinae and Melanderomyiinae. Chandleromyia anomala, n. gen., n. sp., is an anomalously derived Platypezinae from the Cretaceous, and two new species of the diverse Recent genus Lindneromyia are in Dominican amber (L. neomedialis and L. dominicana). Fossils of the relict family Ironomyiidae (with 3 living species from eastern Australia) include two stem-group genera with two new species each, all in Burmese amber: Palaeopetia dorsalis and P. terminus, Proironia (n. gen.) gibbera and P. burmitica. All other species of Palaeopetia are compression fossils from the Cretaceous of Asia and Eurasia. For Phoridae, a new defining feature is a stridulatum on the procoxa and profemur in both sexes, occuring in most fossil taxa where observable. New sciadocerines include Eosciadocera pauciseta, n. sp., a very large species in Baltic amber, and two stem groups in Burmese amber, Prophora dimorion, n. gen., n. sp., and a very small, undescribed taxon. Archiphora pria Grimaldi and Cumming in Turonian-aged New Jersey amber is transferred to Hennigophora Brown, based on evidence from a new specimen. Prioriphorinae (not taxonomically treated here) is a paraphyletic, Cretaceous grade to the very diverse, crown-group radiation of Euphorida that occurred in the Cenozoic. Two syrphoids occur in Burmese amber: Prosyrphus thompsoni, n. gen., n. sp. (an apparent stem group to the Syrphidae), and Aschizomyia burmensis, n. gen., n. sp. (with more ambiguous affinities). Several immatures of undetermined family are reported, one a probable phorid larva. No definitive Schizophora are yet known from the Cretaceous.