Abstract. Using a dynamic power spectral analysis technique, the time-varying nature of solar periodicities is investigated for background X-ray flux, 10.7 cm flux, several indices to UV chromospheric flux, total solar irradiance, projected sunspot areas, and a sunspot blocking function. Many prior studies by a most of authors have differed over a wide range on solar periodicities. This investigation was designed to help resolve the differences by examining how periodicities change over time, and how the power spectra of solar data depend on the layer of the solar atmosphere. Using contour diagrams that show the percent of total power over time for periods ranging from 8 to 400 days, the transitory nature of solar periodicities is demonstrated, including periods at 12-14, 26-28, 51-52, and approximately 154 days. Results indicate that indices related to strong magnetic fields show the greatest variation in the number of periodicities, seldom persist for more than three solar rotations, and are highly variable in their frequency and amplitude. Periodicities found in the chromospheric indices are fewer, persist for up to 8-12 solar rotations, and are more stable in their frequency and amplitude. An additional result, found in all indices to varying degrees and related to the combined effects of solar rotation and active region evolution, is the fashion in which periodicities vary from about 20 to 36 days. I conclude that the solar data examined here are both quasi-periodic and quasi-stationary, with chromospheric indices showing the longest intervals of stationarity, and data representing strong magnetic fields showing the least stationarity. These results may have important implications to the results of linear statistical analysis techniques that assume stationarity, and in the interpretation of time series studies of solar variability.