This paper is concerned with the predator-prey equations simulating an immune response which G. I. Bell and G. H. Pimbley, Jr. studied. In [1], G. H. Pimbley, Jr. has showm that the a_<1->branching of the periodic solutions of this equations appears. In this paper, it will be shown that the λ_<1-> and λ_<2->branching appears under more restricted conditions.