This paper analyzes for the first time a two-loop sliding-mode control (SMC) of a high-order converter supplying a constant power load (CPL). The converter is a single-switch quadratic buck structure (QBC) interfacing a domestic 380 V DC bus to a CPL requiring a regulated voltage of 48 V DC. The converter is unstable in the absence of control and even after the insertion of an inner loop based on SMC of the input inductor current. The addition of an appropriate linear outer loop establishing the reference to the inner loop stabilizes the system and provides output voltage regulation. The regulated QBC shows a fast recovery of the output voltage with negligible overshoot in response to step-type changes of the output power or the input voltage. It is also shown that the implemented regulator for CPL supply can be used directly in the case of a constant current load (CCL) or a constant resistance load (CRL) resulting in similar performance to the CPL case. PSIM simulations and experimental results in a 400 W prototype are in good agreement with theoretical predictions.