In this article we present a detailed theoretical analysis of the behavior of our artificial hormone system. The artificial hormone system (AHS) is part of an organic middleware for mapping tasks on an heterogeneous grid of processing elements. The AHS works completely decentral - each processing cell decides for itself if it is best suited for a task and interacts with the other processing cells via ”hormone” messages. As there is no central element the stability of the system can not be controlled by a single processing element, instead the hormone values have to be chosen carefully to guarantee system stability. We will present upper and lower bounds which have to be met to guarantee system stability.