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We have studied the features of intrinsic Josephson junction stacks in the c-axis direction in highly Pb-substituted (Bi/sub 1-x/Pb/sub x/)/sub 2/Sr/sub 2/CaCu/sub 2/O/sub y/ (with x/spl ges//spl sim/0.2) single crystals exhibiting multiple branches with hysteresis on the I-J characteristics. For the mesa of the single crystal with x=/spl sim/0.2, as the self-field effects on the fluxon motion in the Intrinsic Josephson junctions, the flux flow branch and the zero field step were successfully observed in addition to the supercurrent at zero voltage and the multiple resistive branches. Moreover, their ac Josephson effect was also confirmed by observation of the microwave-induced Shapiro step. These results imply the existence of intrinsic Josephson effects in the single crystals with x/spl ges//spl sim/0.2.