The men, who were arrested in Bradford yesterday, have been bailed until December.
National Crime Agency officers quizzed the men on suspicion of trafficking for the purposes of sexual exploitation.
The offences are alleged to have involved two girls, aged 16 and 17.
The National Crime Agency launched Operation Stovewood, an investigation into child sexual exploitation in Rotherham between 1997 and 2013, after an independent report suggested 1,400 children were abused while those in authority failed to act.
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So far, nine arrests have been made as part of the operation.