He was one of the signatories of the Novi Sad agreement on joint Serbo-Croatian language in 1954.
He published more than 600 works, including the monumental two-volume Savremeni srpskohrvatski jezik: gramatički sistemi i književnojezička norma ("The modern Serbo-Croatian language: grammatical systems and the literary language norm"; Belgrade, 1964–1969).
Together with Ljudevit Jonke he co-edited the first joint Serbian and Croatian orthography book (Novi Sad - Zagreb, 1960).
Stevanović also edited journals Srpski dijalektološki zbornik, Južnoslovenski filolog and Naš jezik.
He was a full professor (since 1951) and the head of the Department of South Slavic languages and General Linguistics, at the Faculty of Philosophy in Belgrade.