A principal means of transmitting intracellular calcium (Ca2+) waves at junctions between astrocytes involves the release of the chemical transmitter adenosine triphosphate (ATP). A model of this process is presented in which activation of purinergic P2Y receptors by ATP triggers the release of ATP, in an autocrine manner, as well as concomitantly increasing intracellular Ca2+. The dependence of the temporal characteristics of the Ca2+ wave are shown to critically depend on the dissociation constant (K(R)) for ATP binding to the P2Y receptor type. Incorporating this model astrocyte into networks of these cells successfully accounts for many of the properties of propagating Ca2+ waves, such as the dependence of velocity on the type of P2Y receptor and the time-lag of the Ca2+ wave behind the ATP wave. In addition, the conditions under which Ca2+ waves may jump from one set of astrocytes across an astrocyte-free lane to another set of astrocytes are quantitatively accounted for by the model. The properties of purinergic transmission at astrocyte junctions may determine many of the characteristics of Ca2+ propagation in networks of these cells.