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Below, I provide a list with all the Machimus/Tolmerus species I managed to find that occur in Greece (bold) and surrounding regions (Asia Minor, Balkans, Caucasus and Middle East). I added these regions too, because, what I usually see when examining Diptera specimens from Lesvos island is that they consist a "mix" with prevelant Caucaso-Levant elements and a few European ones. Also, I noted that I miss Becker's 1923 monograph from my archive, which contains a lot of Turko-Levant species (Engel omits all of Becker's species from his work). As such, it is very possible that if these specimens belong to a known species, it may be one described in this work!

Machimus annulipes (Brullé, 1832) (Eastern Europe, Central Asia, Turkey, Israel)
Machimus aradensis Theodor, 1980 (Israel)
Machimus araxanus Richter, 1963 (Caucasus)
Machimus aridus Lehr, 1999 (European Russia)
Machimus armeniacus Richter, 1963 (Caucasus)
Machimus armipes Becker in Becker & Stein, 1913 (Central Asia, Iran)
Machimus arthriticus (Zeller, 1840) (Europe)
Machimus biljici Adamovic, 1959 (Yugoslavia)
Machimus caliginosus (Meigen, 1820) (Central & Eastern Europe, Turkey)
Machimus chaldaeus Janssens, 1961 (Iraq)
Machimus chrysitis (Meigen, 1820) (Eastern Europe)
Machimus cinerarius (Pallas in Wiedemann, 1818) (European Russia)
Machimus cyanopus (Loew, 1849) (Central & Eastern Europe, Turkey)
Machimus decipiens Theodor, 1980 (Syria)
Machimus dubiosus Becker, 1923 (Yugoslavia, Greece)
Machimus elegans (Loew, 1849) (Turkey, Iran)
Machimus erevanensis Richter, 1963 (Caucasus)
Machimus fimbriatus (Meigen, 1804) (North Africa, Europe, Turkey)
Machimus funebris Theodor, 1980 (Israel)
Machimus gonatistes (Zeller, 1840) (Europe, North Africa)
Machimus gratiosus Loew, 1871 (Turkey, Iran)
Machimus hierosolymae Theodor, 1980 (Israel)
Machimus krueperi Becker, 1923 (Greece)
Machimus largus Richter, 1963 (Caucasus)
Machimus leucocephalus Janssens, 1968 (Greece, Turkey)
Machimus modestus (Loew, 1849) (Eastern Europe, Turkey, Iran)
Machimus mystacinus Becker, 1923 (Turkey)
Machimus nahalalensis Theodor, 1980 (Israel)
Machimus negevensis Theodor, 1980 (Israel)
Machimus rudis Becker, 1923 (Turkey, Iran)
Machimus rusticus (Meigen, 1820) (Europe, North Africa, Turkey)
Machimus sanctimontis Janssens, 1960 (Greece)
Machimus sareptanus Becker, 1923 (Russia, Turkey)
Machimus setibarbus (Loew, 1849) (Europe, North Africa, Middle East)
Machimus thoracius (Loew, 1849) (Hungary?, Turkey, Iran)

Tolmerus angustifrons (Loew, 1849) (Turkey)
Tolmerus atripes Loew, 1854 (Europe, Turkey)
Tolmerus bolgaricus Lehr, 1981 (Bulgaria)
Tolmerus cingulatus (Fabricius, 1781) (Europe, Turkey, Iran)
Tolmerus costalis (Theodor, 1980) (Israel)
Tolmerus facialis Becker in Becker & Stein, 1913 (Iran)
Tolmerus fuscus (Macquart, 1839) (Russia, Turkey)
Tolmerus hermonensis Theodor, 1980 (Syria)
Tolmerus illucens Becker, 1923 (Syria)
Tolmerus lesinensis Palm, 1876 (Italy, Balkans)
Tolmerus paganus Becker, 1923 (Russia, Turkey)
Tolmerus pauper Becker, 1923 (Russia, Greece)
Tolmerus poecilogaster (Loew, 1849) (Central & Eastern Europe)
Tolmerus pyragra (Zeller, 1840) (Europe)
Tolmerus richterae Lehr, 1981 (Caucasus)
Tolmerus rufostriatus (Theodor, 1980) (Israel)
Tolmerus strymonicus (Tsacas, 1960) (Bulgaria, Greece)
Tolmerus tesselatus (Loew, 1849) (Italy, Russia, Turkey)
Tolmerus tivonensis Theodor, 1980 (Turkey, Israel)
Tolmerus ventriculus Becker, 1923 (Greece)