There is evidence that some animal species have developed physiological and behavioral mechanisms to monitor potential predatory threats during rapid eye movement sleep (REMS). Nevertheless, it has not been reported in arboreal primates. The present study analyzed the sleeping postures, as well as the electromyographic and electroencephalographic (EEG) activities during three conditions: REMS, non-REMS (N-REMS), and wakefulness in spider monkeys. The study included six monkeys, whose EEGs were recorded at the O1-O2, C3, C4, F3, and F4 derivations to analyze relative power (RP) and interhemispheric, intrahemispheric, frontoposterior, and central-posterior coherence of frequency bands, which has been considered an index of arousal states. The bands analyzed were theta (4.0-7.0 Hz), alpha1 (8.0-10.5 Hz), alpha2 (11.0-13.5 Hz), and beta (14.0-30.0 Hz). Spider monkeys adopt a vertical posture during sleep, and in REMS a lack of muscular atonia was observed. The RP of the alpha bands at O1-O2 was higher during REMS than that during wakefulness, N-REMS1, and N-REMS2. At the C3 derivation, the RP of alpha1 was higher during REMS than that during N-REMS2. The RP of both alpha bands at the F4 derivation was higher during REMS than that during wakefulness, whereas REMS was characterized by a higher coherence between the F3 and O1-O2 derivations of the alpha2 band. These prevalences and the higher coherence of alpha bands during REMS could represent a correlate of behavioral traits and activated cortical areas related to a possible arousal state in spider monkeys while sleeping.