Approximate stability boundaries for Constant ON-Time buck converters are derived and verified against numerical results obtained by bifurcation analysis. These boundaries are given as analytical expressions involving the main Constant ON-Time (COT) buck converter parameters. They allow the designer to avoid the appearance of the pulse bursting phenomenon. A case study is proposed having in mind automotive applications, which are charaterized by a wide input-voltage range. The input-voltage and the output-capacitor equivalent series resistance, that is typically poorly controlled for some types of capacitors, were chosen as bifurcation parameters.