Abstract
The purpose of the present paper is to prove some results concerning symmetric generalized biderivations on prime and semiprime rings which partially extend some results of Vukman [7]. Infact we prove that: let R be a prime ring of characteristic not two and I be a nonzro ideal of R. If Delta is a symmetric generalized biderivation on R with associated biderivation D such that [Delta(x, x), Delta(y, y)] = 0 for all x, y is an element of I, then one of the following conditions hold
1. R is commutative.
2. Delta acts as a left bimultiplier on R.