The German term is Blasmusik. You will find some English-language works in the bibliography of the German-language Wikipedia entry. (the English-language Wikipedia equivalent is Anglo-American-centric).
The Wikipedia article gives the earliest historic origin in a 36,000 year old flute (worked from a swan bone) found near Blaubeuren in the Swabian Jura. That’s probably a bit of a stretch - oompah bands in the modern configuration are mostly a 19th century development. The repertoire is subject to continual delevopment BTW - last year at a village festival I sat through a collection of ABBA songs arranged for oompah band, consuming bratwurst meanwhile (subject of another thread of yours 
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Thank you for your fast and funny answer. I can’t read the German link (yet), and the english Wikipedia doesn’t have it in english. so… if you have any other good sources about the modern band and music- such as how many players, what kind of instruments they are playing, who was the inventor in the 19th century etc.- I will be more than happy. 
anat, in the German Wiki article, go down to where it says “Vereinigte Staaten von Amerika” (that’s USA): it lists books in English which include information on this kind of music.