Prior investigations attempted to determine the relative influence of advection and convective processes on ozone and water vapor distributions in the tropical tropopause layer (TTL) through analyses of tracers, related physical parameters (e.g., outgoing long‐wave radiation, precipitable water, and temperature), or with models. In this study, stable laminae in Southern Hemisphere Additional Ozonesonde Network (SHADOZ) ozone profiles from 1998 to 2007 are interpreted in terms of gravity waves (GW) or Rossby waves (RW) that are identified with vertical and quasi‐horizontal displacements, respectively. Using the method of Pierce and Grant (1998) as applied by Thompson et al. (2007a, 2007b, 2010, 2011), amplitudes and frequencies in ozone laminae are compared among representative SHADOZ sites over Africa and the Pacific, Indian, and Atlantic oceans. GW signals maximize in the TTL and lower stratosphere. Depending on site and season, GW are identified in up to 90% of the soundings. GW are most prevalent over the Pacific and eastern Indian oceans, a distribution consistent with vertically propagating equatorial Kelvin waves. Ozone laminae from RW occur more often below the tropical tropopause and with lower frequency (<20%). Gravity wave and Rossby wave indices (GWI, RWI) are formulated to facilitate analysis of interannual variability of wave signatures among sites. GWI is positively correlated with a standard ENSO (El Niño–Southern Oscillation) index over American Samoa (14°S, 171°W) and negatively correlated at Watukosek, Java (7.5°S, 114°E), Kuala Lumpur (3°N, 102°E), and Ascension Island (8°S, 15°W). Generally, the responses of GW and RW to ENSO are consistent with prior studies.