This is the first study of a real physical kneed bipedal robot that exhibits passive dynamic running (PDR). Passive dynamic walking (PDW), which has its roots in the pioneering research of McGeer, intrinsically offers not only nonlinear phenomena such as the pull-in effect and period-doubling bifurcation, but also offers an extremely interesting phenomenon that facilitates the engineering of a highly efficient walking robot. In recent years, a wide variety of verification experiments in PDW were performed using actual devices. In contrast, however, very few studies addressed PDR. In the present study, we developed a two-dimensional real physical passive dynamic running biped with knees. The device stands 400 mm tall and weights 4.8 kg. By carefully designing the properties of the elastic elements implemented into the hip joints and the stance legs in the present device, we achieved stable passive dynamic running of 36 steps. The device runs at about 0.83 m/s down a 0.22 rad slope. To the best of our knowledge, this is a first report of such a performance. This result is expected to prove useful not only for designing human-like natural and efficient bipedal robots, but also for understanding the principles underlying bipedal locomotion.