If convicted, the pair could face jail and then deportation from the United Arab Emirates, which walks a delicate line between keeping its Muslim identity and maintaining a successful tourism industry.
Rebecca Blake and Conor McRedmond both denied charges of "breach of honour with consent" and committing "an indecent act in a taxi" when they appeared in court.
They pled guilty to a third charge related to the consumption of alcohol, their lawyer said after the hearing. The judge postponed the next hearing to November 1.
There have been several cases in recent years of Westerners accused of violating decency laws in Dubai, the most cosmopolitan of the seven-member United Arab Emirates federation.
Expatriates comprise more than 90% of the UAE's population, attracted by tax-free earnings.