We present a Nyquist stability criterion, together with step time responses, for the small-signal equivalent circuit model of common-source-configured carbon-nanotube (CNT) field-effect transistors (CNTFETs) made of 100 CNTs at 10-nm pitch as well as single CNTs, for the first time. In this analysis considering tube-to-tube variations in CNTs' diameters, dependence of the degree of relative stability on CNT dimensions is acquired. Simulations show that the step responses for both types of CNTFETs, unlike those for CNT/GNR-based local interconnects, pose multiharmonic oscillations. Amplification of such harmonics by CNTFET can cause instability.