This study examined implicit and explicit memory for words presented during Rapid Eye Movement (REM) sleep. Ten subjects were presented two lists of twenty words: one list just before they fell asleep and the other during the second and the third periods of REM sleep. The next morning, they were given an implicit memory task (word stem completion) and an explicit memory task (recognition). While they were carrying out these tests, their electrodermal activity was recorded. The implicit task showed no learning effect for either list of words, whereas the explicit task showed a learning effect only for the list presented before sleeping. Moreover, the recording of the skin conductance variations gave no significant results. Thus, no evidence of implicit memory during REM sleep was observed.