Results of an analysis of towed thermistor chain measurements in the western North Atlantic indicate that over a wide range of one-dimensional wave numbers and for frequencies down to within a fraction of the inertial frequency the internal wave spectrum may be adequately represented by the Garrett and Munk (1972, 1975) model. However, the spectral shape very near the inertial frequency (ω≲ (2)1/2f) predicted by the model is markedly different from that inferred from the data considered here. This observation has serious implications insofar as purely spatial (i.e., two-dimensional vertical-horizontal) modeling is concerned, and it is concluded that a new space-space model for random temperature structure, separate but evolving from the Garrett and Munk model, is needed. The basis properties of such a model are described, but more work will be required before a definitive space-space model for random temperature structure in the ocean can be established.