Diptera of the families Empidae, Asilidae, and Tipulidae have been found as far back as the Lias.    From Wordnik.com.  [Darwinism (1889)] Reference

I collected, in northeastern Colorado, a very large (ca. 1 inch) species of robber fly (family Asilidae).    From Wordnik.com.  [VERBATIM: The Language Quarterly Vol XV No 1] Reference