The first objective of this work was to obtain values for the rates at which continental erosion can smooth out or remove the topographic expression produced by orogeny. The dominant part is played by mechanical erosion, which acts most strongly in regions of large topographie expression. Chemical erosion depends strongly on precipitation or run off in individual river drainage basins, but because most continents have very similar average rainfall, chemical erosion is fairly uniform for continental sized areas, and will succeed in planing down all continents to a level peneplain if given enough time. The exception to this rule is Australia, which has a very low chemical erosion rate because of its dryness. The time constants for mechanical and chemical erosion so obtained vary between ab out 30 and 300 My depending on the continent and the assumptions made. Mountain building occurs throughout the geological time-scale, but at a non-uniform rate. Although there will not be a balance between erosion and mountain building over a short time-scale, due to the non-uniform rate of mountain building, the long-term situation must be that the two phenomena should balance out. It is shown that the freeboard of continents will respond to the long-term balance between mountain building and erosion. An expression has been derived for the average continental elevation in which the rate of mountain building depends on the rate of radiogenic he at production within the earth. It is shown that relatively small changes in average elevation above sea level of a few hund red metres are predicted to have occurred since the beginning of the Proterozoic. As mountain building is predicted to decrease on average with time, because of the reduction in internal heat generation, and as erosion is dependent on the average elevation, this average elevation will decrease slowly through time, the opposite of what some workers have predicted. A more complicated model of mountain building is then investigated, in which one component of