LetR be a *-ring. We study an additive mappingD: R → R satisfyingD(x2) =D(x)x* +xD(x) for allx ∈ R.It is shown that, in caseR contains the unit element, the element 1/2, and an invertible skew-hermitian element which lies in the center ofR, then there exists ana ∈ R such thatD(x) = ax*− xa for allx ∈ R. IfR is a noncommutative prime real algebra, thenD is linear. In our main result we prove that a noncommutative prime ring of characteristic different from 2 is normal (i.e.xx* =x*x for allx ∈ R) if and only if there exists a nonzero additive mappingD: R → R satisfyingD(x2) =D(x)x* +xD(x) and [D(x), x] = 0 for allx ∈ R. This result is in the spirit of the well-known theorem of E. Posner, which states that the existence of a nonzero derivationD on a prime ringR, such that [D(x), x] lies in the center ofR for allx ∈ R, forcesR to be commutative.