An analytic study is made of the electrostatic mode structures which exist between the upper-hybrid cut-off and the plasma resonance in a plasma in which the zero-order density gradient points along the magnetic field. In general the solutions consist of long-wavelength cold modes which are converted to short-wavelength Bohm-Gross modes near plasma resonance. However, there exist certain discrete angles of propagation at which finite solutions exist that can be described solely in terms of cold plasma theory. The relevance of these processes to resonant absorption experiments in the auroral ionosphere is considered. A brief study is made of the changes produced by a finite angle between the density gradient and the magnetic field. The possibility of finding analogous low-frequency structures is also investigated.