We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${ abla}_{varepsilon}S=0;and;{ abla}_{varepsilon}R_{varepsilon}=0,;where;S;and;R_{varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.