Reelle algebraische Funktionen mit vorgegebenen Null- und Polstellen

This note continues the investigations of Knebusch on algebraic curves over real closed fields and was initiated by reading 3]. Especially we ask for the existence of real algebraic functions with given zeroes and poles, a question going back to Witt 4]. We study the real nature of coverings of real algebraic curves, and if the covering has degree two, we get algebraic proofs for results, which in the classical case have been obtained by topological methods in 2].