We introduce the following notion. Let N 0 be the set of all nonnegative integers and let = ( ) ∈N 0 be a family of additive mappings of a * -ring R such that 0 = ; D is called a Jordan higher * -derivation (resp., a Jordan higher) for all , ∈ and each ∈ N 0 . It is shown that the notions of Jordan higher * -derivations and Jordan triple higher * -derivations on a 6-torsion free semiprime * -ring are coincident.

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We investigate the additivity and multiplicativity of centrally extended higher derivations and show that every centrally extended higher derivation of a semiprime ring with no nonzero central ideals is a higher derivation. Moreover, we study preservation of the center of the ring by a centrally extended higher derivation.