  Let A be a C*-algebra and d from A into A** be a continuous linear map. We
assume that d acts like derivation or anti-derivation at orthogonal elements
for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and
ab*=b*a=0. In each case, we characterize the structure of d. Then we apply our
results for von Neumann algebras and unital simple C*-algebras.
