This paper presents two output-capacitor-free low-dropout regulators (LDOs) with nA quiescent current for Internet-of-Things (IoT) applications. The proposed LDO1 combines the dynamic current biasing and the adaptive current biasing techniques for drastically reducing the quiescent current to the nA level while achieving fast transient response. Based on LDO1, the proposed LDO2 adds an inverter-based dynamic loop to further improve the transient response. The prototypes are fabricated in a 65-nm low-leakage CMOS process, with active areas of 0.0042 and 0.0048 m², respectively. Measurement results show that LDO1 and LDO2 consume 30 and 100 nA quiescent current, respectively, with 1 V input, 0.8 V output, and 100 nA load current. Stability analysis shows that both LDOs achieve good stability with load current ranging from 100 nA to 10 mA. With the load current steps from 100 nA to 10 mA in 1-μs transition time, the measured voltage undershoots are 336.8 mV for LDO1 and 196 mV for LDO2. Therefore, we reach a figure-of-merit of 0.00159 ps.