The purpose of this paper is to prove some results concerning symmetric biderivations and symmetric generalized biderivations on prime and semiprime rings which partially extend some results contained in Vukman, J., Symmetric biderivations on prime and semiprime rings, Aequationes Math. 38 (1989), 245-254 and Vukman, J., Two results concerning symmetric biderivations on prime rings, Aequationes Math. 40 (1990), 181-189.