Summary form only given: A distributed-adaptive droop mechanism is proposed for secondary/primary control of dc microgrids. The conventional secondary control that adjusts the voltage set point for the local droop mechanism is replaced by a voltage regulator. A current regulator is also added to fine-tune the droop coefficient for different loading conditions. The voltage regulator uses an observer that processes neighbors' data to estimate the average voltage across the microgrid. This estimation is further used to generate a voltage correction term to adjust the local voltage set point. The current regulator compares the local per-unit current of each converter with the neighbors' on a communication graph and, accordingly, provides an impedance correction term. This term is then used to update the droop coefficient and synchronize per-unit currents or, equivalently, provide proportional load sharing. The proposed controller precisely accounts for the transmission/distribution line impedances. The controller on each converter exchanges data with only its neighbor converters on a sparse communication graph spanned across the microgrid. Global dynamic model of the microgrid is derived with the proposed controller engaged. A low-voltage dc microgrid prototype is used to verify the controller performance, link-failure resiliency, and the plug-and-play capability.