Abstract: By defined holomorphic n-times integrated mild C-existence families and C-semigroups, their relationship with holomorphic mild C₁-exustence families and holomorphic C₁ -semigroups is discussed, respectively. For exponentially bounded cases, this paper gives several Hille-Yosida type conditions for an operator to have (or generate) one of these families of operators and generalize the corresponding results in[1],[2] and[3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.

Key words: holomorphic integrated mild, C-existence families, C-semigroups