The constant on-time current-mode controlled (COT-CMC) switching dc-dc converter is stable, with no subharmonic oscillation in its current loop when a voltage ripple in its outer voltage loop is ignored. However, when its output capacitance is small or its feedback gain is high, subharmonic oscillation may occur in a COT-CMC buck converter with a proportional-integral (PI) compensator. To investigate the subharmonic instability of COT-CMC buck converters with a PI compensator, an accurate reduced-order asynchronous-switching map model of a COT-CMC buck converter with a PI compensator is established. Based on this, the instability behaviors caused by output capacitance and feedback gain are investigated. Furthermore, an approximate instability condition is obtained and design-oriented stability boundaries in different circuit parameter spaces are yielded. The analysis results show that the instability of COT-CMC buck converters with a PI compensator is mainly affected by the output capacitance, output capacitor equivalent series resistance (ESR), feedback gain, current-sensing gain and constant on-time. The study results of this paper are helpful for the circuit parameter design of COT-CMC switching dc-dc converters. Experimental results are provided to verify the analysis results.