The spectral analysis of unequally spaced data is discussed with reference to two examples of vertical profiles of internal wave displacment. For our examples, a Conductivity, Temperature, Depth probe was used to record temperature from which the wave displacement were determined. Ship heave, amont other causes, resulted in the data being recorded at unequal intervals of depth. Spectral analysis is complicated by unequal data spacing, but the necessity of using an appropriate method is demonstrated by the comparison of results from two such methods with those from two analyses based on equispaced techniques. The equispaced analyses produce results consistent with the currently accepted picture of internal wave spectra but not with the results from the analyses which take account of the unequal spacing. This has important ramifications for oceanographic spectral analysis procedure. It is clear from our examples that the variability inherent in the unequal spacing has a much greater effect than one might at first imagine. In particular, our examples suggest that important structure at higher wave numbers may be totally lost if inappropriate methods of analysis are used. ¿ American Geophysical Union 1988