We report on the continuous feedback operation of a two-stage dc Superconducting Quantum Interference Device (SQUID) system in which one SQUID works as a low-noise preamplifier to read out a second low-noise sensor SQUID. We first flux-locked the readout SQUID and measured the characteristics of the sensor SQUID, including its current-voltage characteristics, current-flux characteristics, and noise spectrum. We then investigated how the two SQUIDs could work together by simultaneously flux-locking both the sensor and the readout SQUIDs. With this two-SQUID flux-locking scheme, we recovered the noise spectrum of the sensor SQUID to within 4%. We discuss how to understand and optimize the two-stage SQUID feedback system.