Stephen McLaughlin, 34, and Timothy Murphy, 33, are accused of conspiring to facilitate illegal entry into the UK.
The men, both from Londonderry, Northern Ireland, spoke only to confirm their names and personal details when they appeared during separate hearings at Chelmsford magistrates’ court in Essex.
They are charged with conspiring with each other and “with other persons unknown” to “clandestinely convey 35 Afghan nationals by sea in to an English port which facilitated the commission of a breach of immigration law”.
The alleged offence is said to have taken place between 1 and 17 August.
The men sat quietly in the dock as they were each remanded in custody until a hearing at Basildon crown court on a date to be set during the week beginning 17 November.
Meet Singh Kapoor, 40, from Afghanistan, was found dead inside the container at Tilbury Docks on 16 August.
He was among a group of 35 immigrants, the rest of whom survived the ordeal, including 13 children.
The group, whose ages ranged from one to 72, are believed to have fled Afghanistan after suffering persecution.