Simon Radford, Joshua Finbow, Craig Stoner and Darren Smalley were in Nova Scotia to play in a hockey tournament with local Armed Forces personnel when they were arrested in April.
The Crown alleges the members of the Royal Navy participated in a "group sexual assault'' on April 10 inside a barracks at CFB Shearwater, a military base in Halifax.
The men have not entered pleas in the case.
None of the allegations has been proven in court.
Court heard Tuesday that Smalley has elected to be tried by a judge and jury in Nova Scotia Supreme Court.
Under the Criminal Code, when two or more people are charged with the same offence, if one elects a trial by judge and jury then the rest must follow suit, Crown attorney Scott Morrison said outside court.
The four men are out on bail after being transferred from a Halifax military base to one in Alberta.
A provincial court judge granted a change in bail conditions last month allowing them to move to CFB Suffield where there is a British army training unit.
Smalley was the only one of the four men to appear in court Tuesday.
Outside court, Morrison said three of the men, Radford, Finbow and Stoner, have applied for changes to their bail conditions to allow them to return to the United Kingdom. Morrison said the Crown will oppose the application at a court hearing on Aug. 11.
"The Crown's perspective is that we've created a bail plan that allows them a substantial amount of freedom, but keeps them in the country so that we can ensure they'll attend court to be dealt with according to law," Morrison said.
Defence lawyer Mark Knox, who represents Finbow, said the men should be allowed to leave the country.
"They want to return to their homes to work there," he said outside court. "They want to go home, as anybody would."