A parabolic wave theory is considered in which the energy flux through an elemental aperture is required to lie in directions measured relative to a ’’local’’ principal propagation direction that can be termed narrow angled. This can be compared to the more commonly encountered theory, in which a ’’global’’ principal propagation direction is used. A propagation model is then developed which is formulated in terms of an acoustic field measure termed the acoustic intensity angular spectral density. The relationship between this propagation model and the geometric theory is considered, with the latter being recovered in the appropriate limit. A sample calculation is carried out for the behavior of a beamed signal in the vicinity of a point caustic.