We have performed specific heat, ultrasound, and magnetoresistivity measurements examining the dense Kondo system Ce 0.5 La 0.5 B 6 . The results obtained support the view that in the case of Ce 0.5 La 0.5 B 6 a nonmagnetic state ͑the Kondo nonmagnetic state͒ exists due to the dense Kondo effect under low-temperature and low-field conditions. We have identified two characteristic temperatures in Ce 0.5 La 0.5 B 6 . One is the Kondo temperature T K (5.5ϳ11 K), and the other is T QC (ϳ1 K) which denotes the binding energy for the electric quadrupolar cancellation. In the Ce x La 1Ϫx B 6 system, T K is strongly dependent on the Ce concentration, whereas T QC is almost independent of it. The present results strongly suggest that phase IV exists in the range of 0.6ϽxՇ0.75. The low-temperature specific heat of Ce 0.65 La 0.35 B 6 in phase IV was found to be in proportion to T 2 and this is difficult to interpret in terms of antiferromagnetic ordering. The appearance of phase IV may arise from the pronounced discrepancy between T K and T QC .