It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{xi}$ which are weaker than ${ abla}R_{xi}$ = 0. Under further condition $Sphi={phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.