The authors extend to generalized derivations some known results for derivations acting on prime rings. Let \(R\) be a prime ring with center \(Z\) and extended centroid \(C\). Call \((d,\alpha)\) a generalized derivation of \(R\) when \(\alpha\in\text{Der}(R)\), \(d\colon R\to R\) is additive, and \(d(xy)=d(x)y+x\alpha(y)\) for all \(x,y\in R\). Among the results in the paper that the authors prove for \((d,\alpha)\) are: \(d=0\) when either \(d([x,y])=0\) for all \(x,y\in R\), \(d\) is a homomorphism, or \(d\) is an anti-homomorphism; if \([x,d(x)]=0\) for all \(x\in R\) then \(d(x)=qx\) for some \(q\in C\); if \([a,d(R)]\subseteq Z\) for some \(a\in R\) then \(R\) is commutative, \(\alpha(Z)=0\), or \(a\in Z\). The authors also characterize \((d,\alpha)\) when \(d^2(R)\subseteq Z\) and when \(R\) is not commutative and \(\text{char\,}R\neq 2\).