Let A be a C-algebra, and let δ : A → A∗∗ be a continuous linear map. We assume that δ acts like a derivation or like an anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab = 0, ab = 0, ab = 0, ab = ba = 0 and ab = ba = 0. In each case, we characterize the precise form of δ.
