Time trends and periodic cycles in REM sleep eye movements were examined in 6 functional and 6 mongoloid adolescent retardates. Both groups of subjects showed approximately equal percentages of linear trends, quadratic trends, linear and quadratic trends, and absence of trend. The eye movement time-series were subject to an orthogonal spectral analysis. In both groups of subjects, peak spectral estimates generally occurred at 10.6- or 21.3-min periods. Following this, the eye movements of the longest REM periods (and one long period of pre-sleep wakefulness) were subject to a least-squares spectral analysis. This analysis yielded estimates ranging from 22 to 44 min. Eye movements lacked the ultradian organization previously reported for eye movements of normal subjects. These results imply that the ultradian organization of REM sleep and the ultradian organization of eye movements may be independent.