We discuss hysteretic behaviors of dilute viscoelastic polymeric fuids with moment-closure approximation approach in extensional/enlongational fows. Polymeric fuids are modeled by the nite extensible nonlinear elastic (FENE) spring dumbbell model. Hysteresis is one of key features to describe FENE model. We here investigate the hysteretic behavior of FENE-D model introduced in [Y. Hyon et al., Multiscale Model. Simul., 7(2008), pp.978-1002]. The FENE-D model is established from a special equilibrium solution of the Fokker-Planck equation to catch extreme behavior of FENE model in large extensional fow rates. Since the hysteresis of FENE model can be seen during a relaxation in simple extensional fow employing the normal stress/the elongational viscosity versus the mean-square extension, we simulate FENED in simple extensional fows to investigate its hysteretic behavior comparing to FENE-P, FENE-L [G. Lielens et al., J. Non-Newtonian Fluid Mech., 76(1999), pp.249{279]. The FENE-P is a well-known pre-averaged approximated model, and it shows a good agreement to macroscopic induced stresses. However, FENE-P does not catch any hysteretic phenomenon. In contrast, the FENE-L shows a better hysteretic behavior than the other models to FENE, but it has a limitation for macroscopic induced stresses in large shear rates. On the other hand, FENE-D presents a good agreement to macroscopic induced stresses even in large shear rates, and moreover, it shows a hysteretic phenomenon in certain large fow rates.