The authors prove versions of a theorem of E. Posner [Proc. Am. Math. Soc. 8, 1093-1100 (1958; Zbl 0082.03003)] for rings with involution. Let \(R\) be a prime ring with involution *, denote the center of \(R\) by \(Z\), and assume that \(R\) is not an order in a simple algebra four dimensional over its center. Set \(S=\{r\in R\mid r^*=r\}\) and \(K=\{r\in R\mid r^*=-r\}\), and let \(d\) be a derivation of \(R\). The main results of the paper show that if \(xd(x)-d(x)x\in Z\) for all \(x\in S\), or for all \(x\in K\), then \(d=0\). The authors also show that \(d=0\) if \(xd(x)+d(x)x\in Z\) holds for either \(S\) or \(K\).