Hannah Witheridge, 23, from Great Yarmouth, Norfolk, and David Miller, 24, from Jersey, were killed on the island of Koh Tao last September.
Their families have travelled to the nearby island of Koh Samui where Burmese migrants Zaw Lin and Wai Phyo, also known as Win Zaw Htun, stand charged with murder and rape.
The investigation into the deaths has been marred by confusion and allegations of police incompetence.
The defendants are said to have confessed under pressure from local police shortly after the killings but have since retracted those statements.
Just before the trial started the defence claimed new evidence supplied by British authorities could prove their innocence.
Nakhon Chompuchat, defending, said he is in possession of crucial DNA evidence found on the victims: “We have received information from Britain that shows inconsistencies in the prosecution case. It is significant evidence.”
The first policeman on the murder scene described getting a call at 6.30am that day informing him two bodies had been found on the beach. “I found a man’s body lying on the beach with seawater lapping his body,” said Lieutenant Jakrapan Kaewkao, a witness for the prosecution.
“Then I found the woman’s body behind the rocks.”
He said the bodies, both of which were mostly unclothed, were several metres apart and that Witheridge’s bore signs of physical assault. He also said the rocks were spotted with blood.
Earlier Chompuchat, the defence lawyer, said he hoped the trial would be a just one. “We hope the truth will be revealed,” he said. “We hope the mechanism of justice in Thailand... will have the same standards of international countries.”
While journalists were initially allowed into the small courtroom, they were moved out to make room for others attending the trial, including relatives and diplomats.
In a statement before the trial began, Miller’s family said: “The act which ended David’s life devastated our family and his friends.
“Just hours before he died David was talking to us with his usual enthusiasm, describing the beauty of Koh Tao and the friendliness of the Thai people.”