Аннотация:We consider a model of gradual heating of the lithosphere against a background of slight extension in order to analyze the character that its igneous activity might take. Analysis indicates that two different cases of igneous activity should occur: 1) igneous activity in a thick lithosphere with two highly viscous (or brittle) crustal and subcrustal layers; 2) igneous activity in thin lithosphere with one highly viscous upper crustal layer. The model applies to rift zones developing under conditions of relatively slight extension. With high rates of extension the mean effective viscosity of the lithosphere rises markedly. This should result in its splitting and to the development of deep fissure rifts, and, if the rifting process is prolonged, to rapid conversion of the continental rift into an oceanic rift.