Process philosophy, as formulated primarily by Alfred North Whitehead, is (at the simplest level) a method of understanding the universe as a collection of processes rather than things; it emphasizes change as the one universal constant. 
As one Process-related website puts it,
…what traditional philosophy would call an enduring substance, Whitehead calls a succession or “route” of actual occasions with a common characteristic. Change is explained by the creative contribution of each occasion in the series, and endurance is explained by common qualities which are inherited from antecedent occasions. The flux and stability of all things are explained in this way, whether they be electrons, rocks, plants, mammals, or men. Man is an extremely complex route or “nexus” of occasions with memory, imagination, and heightened conceptual feelings. 
Charles Hartshorne (and others) took this basic idea and applied it to Christian theology, attempting to reconcile the dissonance between Biblical and Neoplatonic philosophy (most especially between the two conceptions of God as the Absolute or Unconditioned, and as a personal deity) that has been near the center of Christian thought since Saint Augustine.  However, I believe that the “process” idea, particularly in combination with a spiritually-oriented application of systems theory, can be a valuable tool for deepening the discourse of polytheology.
What I propose is more than simply the re-application or co-opting of this model to a polytheistic context; process theology as it stands today answers questions in Christianity, and to a lesser extent in Judaism, that simply don’t occur in most forms of polytheism (although I suppose they might in certain types of “emanationist” polytheology, where the Gods are seen <b>simply</b> as self-expressions of an underlying One). Rather, in the next post I hope to use the creative synthesis of systems and process theory to speculate on the nature of the Gods as traditionally understood in my own primary religious milieu (Hellenistic polytheism), and to look for areas of special moral concern arising from that speculation.
To be clear: although the theological “language” I use is Hellenistic, because that is my particular religion, I do not in any way see a natural systems theology as bound to a particular religion, culture, pantheon or tradition. In fact, by its very nature it must be universally applicable, or it is meaningless.
 http://www.religion-online.org/showarticle.asp?title=1489, § 2. The Doctrine of God