After a brief recapitulation of the mathematical theory of the dynamics of viscous layers with contrasted density in the field of gravity, the instability of a buoyant stratum buried deep in the mantle is discussed. Such layers are particularly interesting from the point of view of global tectonics because of the large dominant wavelength which they sometimes develop. Under certain conditions the wavelength is several thousand times the thickness of the layer. For layers only a few km thick then, their wavy ascent may cause crustal disturbances on the scale of oceans and continents, contributing to continental drift and the opening-up of oceans. The rate of rise calculated varies from 0.002 cm/y to no less than 247 cm/y. An episodic character of tectonic evolution is predicted because the rate of ascent of a layer increases faster than linearly with its thickness. The buoyant layer is imagined to grow in thickness by an endothermic and exospatic (volume increasing) process such as e.g. the change from spinel-type (Mg, Fe) 2SiO 4 to the olivine-type, due to radioactive heating. Not until the thickness of the layer has reached a minimum value will it start rising with a sensible speed. As the layer thickens further, the rate of rise increases fast and the wavy pattern of the layer amplifies rapidly, developing into independent diapirs which ascend through the mantle and cause tectonic movements in the crust. After the energy of the buoyant diapirs has been exhausted, a period of dynamic quiescence follows until enough radioactive heat develops to produce a new buoyant layer with the minimum thickness. Experimental models imitating the rise of a low-density layer in the mantle are presented, and so are models imitating the spreading of a low-density pillow (mushroom) underneath the Mid-Atlantic Ridge, and the consequent drifting apart of the New and the Old worlds. Fusion and other phase changes due to pressure relaxation in a rising diapir in the mantle is discussed. This is found to be a realistic magma-producing process capable of melting a major fraction of the rising crystalline body.