In the present paper we have examined the applicability of dimensionless and invariant numbers (DN & IN) to the analysis of the cardiovascular system of mammals, whose functions were measured at standard metabolic conditions. The calculated IN did not change when we compared these figures with those obtained in dogs while they were submitted to graded exercise on a treadmill. In both instances, rest and exercise, the constancy of the IN prevailed, in accordance with Cannon's principle of "homeostasis" (1929). On the contrary, when dogs were examined during a standardized hypovolemic shock, we observed a breakdown of the IN, and the resulting DN evolved as a reliable index of the condition of "heterostasis" as defined by H. Selye. The robustness of the homeostatic regulations is based on high-gain integral feedback mechanisms, while "heterostasis" could be associated with low-gain integral feedback processes, when organisms are submitted to unitary step disturbances or to changes of the set-point at the entrance of the feedback loop.