When a prerecorded cross-beam hologram is reconstructed (so-called edge-lit readout) with a uniform plane wave and a point source, the resulting exact solutions reveal Bessel-function-type diffracted beam profiles, which are fundamentally modified under weak propagational diffraction. The case of a profiled beam readout with propagational diffraction may be analyzed using a transfer function approach based on 2-D Laplace transforms. In a second series of investigations, dynamic readout from a cross-beam volume hologram recorded with two orthogonal uniform plane waves is considered for various dependences of the refractive index modulation with intensity. Typically, refractive index profiles that are proportional to the intensity (as in the case of Kerr-type media or photorefractives with predominantly photovoltaic effect) and to the derivative of the intensity (as in diffusion-dominated photorefractives) are considered. Two-dimensional nonlinear coupled equations are developed for the two (Bragg) orders for both cases. Closed form solutions are obtained for the first case, indicating only nonlinearly induced self and cross-phase coupling. A simple experiment involving simultaneous recording and readout using photorefractive lithium niobate crystal indicates beam profile distortion, which may be expected in such 90-deg geometries.