Broch was born in Horten, and was a brother of children's writer
Lagertha Broch,
zoologist Hjalmar Broch, and social worker
Nanna Broch. He married Ninni Henriette Trampe in 1896. It was in Jagić's journal
Archiv für slavische Philologie where he published his first article in 1895, a study of the
Ubľa dialect. In the following years Broch made many extensive
dialectological trips in Slavic countries, resulting in studies of Russian, Slovak, Belarusian, and Serbian
Torlak dialects. In his studies of
Russian dialects, Broch was the first to notice and describe dialects with two additional vowels /ѣ/ and /ω/, stimulating further research into the matter, including the influential 1914 study of the village dialect by Broch's close colleague
Aleksey Shakhmatov. Having experience with analysing phonetics of various Slavic dialects, Broch was invited by Jagić to write a volume on the general phonetics of Slavic languages for his
Encyclopedia of Slavic Philology. Published in Russian (1910) and German (1911), it is regarded as Broch's most important scholarly contribution. Broch was the first professor of
Slavic languages at the
University of Oslo, where he taught from 1900 to 1937. He was decorated Commander of the
Order of St. Olav in 1946. He was a member of a number of foreign academies, ==Publications==