The author incorporates delay into an ODE considered by S.-R. Zhou et al. [Theor. Popul. Biol. 67, 23–31 (2005; Zbl 1072.92060)] to obtain
which describes the dynamics of a ratio-dependent predator ()-prey () system. First, the local stability of the positive equilibrium point is studied. is stable for and Hopf bifurcation occurs for , where for . Then the stability and direction of bifurcating periodic solutions is discussed using the normal form theory and center manifold theorem due to [B. D. Hassard and N. D. Kazarinoff, Theory and applications of Hopf bifurcation. Moskva: Mir (1985; Zbl 0662.34001)].