<p>We classify Jordan derivations and Lie derivations of some important classes of alternative rings, namely alternative division rings and split octonion algebras. For these rings, every Jordan derivation that also satisfies a certain additional condition is a derivation. This additional condition is not necessary for associative rings, but is necessary for alternative rings. Also, for these rings, we show that every Lie derivation has the expected form, being the sum of a derivation and an additive function that has image in the center and vanishes on commutators.</p>