Ross Waterhouse, aged 22, of Hyde Park, Leeds, pleaded not guilty to charges of kidnap and rape.
Matthias Buchmeier, 30, of Manor Park, Scarcroft, denied one count of kidnap.
Both men were remanded in custody to stand trial on 3 April. A third man arrested in connection with the incident remains on police bail.
Two men have appeared in court and denied kidnapping and raping a woman who was given a lift from Leeds city centre.