The theory of the boundary layer above a therrmally active inclined terrain, in which the actual height h of the boundary layer is used as length scale, is presented. Analytical solutions for the mean wind and temperature structures are obtained. These solutions are seen to depend on the non-dimensional parameters h/L, A = hs /ys, h/zo , the slope angle u the direction of the geostrophic wind x in addition to z/h. As by-products of these solutions (1) expressions for the similarity theory stability functions a, b and c are obtained which are in agreement with the theoretical expressions of Zilitinkevichand Brost and Wyngaard (2). For slope angles much less than 0.01, u = 0 yields the well-known expressions of Zilitinkevich and Deardorff. The appreciable influence of u and x on the geostrophic drag coefficient and on the crossisobaric angle a is assessed and and presented in graphical form. Finally, a preliminary test which shows that the predicted a is in satisfactory agreement with observations, is also presented.