The phenomenon, known as rapid facial mimicry, is an unconscious response that occurs when two animals are interacting.
Researchers showed that geladas (Theropithecus gelada), a type of Old World monkey, found in the Ethiopian Highlands, with large populations in the Semien Mountains, show facial mimicry during play - particularly mother-infant pairs.
The curious ability may have a common evolutionary root among primates, the researchers said.
"This mimicry relates to an internal emotional connection," said neuroscientist Pier Francesco Ferrari of the University of Parma in Italy, who co-authored the study published in the journal Scientific Reports.
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The researchers observed adult and baby geladas at a zoo in Germany during playful interactions. They recorded the play sessions on camera, noting whether the animals imitated each other's facial expressions.
Facial expressions included the "play face," (an open mouth with only the lower teeth exposed), the "full play face" (lips pulled back to expose the upper and lower teeth and gums) and "lip-smacking" (lips smacked together, sometimes with the tongue extended).
The play faces are considered the equivalent of laughter in humans, whereas lip-smacking can have different meanings depending on the context.
The findings show that the mimicking behaviour seen in humans and apes has a counterpart in monkeys. In addition, the similarities between mother-baby interactions in these species suggest a common evolutionary origin.
Rapid facial mimicry is thought to arise from brain areas linking perception and actions. Scientists studying monkeys have found evidence of brain cells known as mirror neurons, which are active both when an animal performs an action and when it watches another animal doing it.