Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $alpha_1$ and the generalized time constant $ au$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $alpha_1$ and $ au$ changes. We first deal with the root sensitivity to the perturbation of $alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $ au$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.