Lee and Ho are already serving jail terms for their roles in unauthorised protests in 2019.
Chow and four others arrested this week were also charged with failing to comply with the requirement to provide information for a national security investigation.
Representatives from the British, Swedish and German consulates were in the courtroom before the hearing started.
The alliance, chairman Lee Cheuk-yan, vice chairman Albert Ho and vice chairwoman Chow Hang Tung face charges of “inciting subversion of state power,” the organisation said on its Facebook page. Other members are accused of not providing information requested by national security officials.
Dominic Raab, Britain’s Foreign Secretary, called the arrests “another chilling demonstration of how the National Security Law is being used by Beijing to dismantle civil society and stifle political dissent in Hong Kong”.
Antony Blinken, US Secretary of State, said the arrests were “politically motivated and constitute a blatant abuse of law by those in power”.
Alliance leaders Albert Ho and Lee Cheuk-yan have already been jailed for pro-democracy protests that rocked Hong Kong in 2019.
The Tiananmen museum has had to close and relocate several times. In June, organisers finally shut its most recent location to “ensure the safety of staff and visitors”.
The alliance moved the museum online in August after a HK$8,000 (£750) fine for operating without a licence. The museum once showed archival footage and sound from the night of the massacre, as well as testimonies from survivors.
There was also information about those killed and subsequent attempts to keep the memory of the crackdown alive, including large pictures of the annual vigil in Hong Kong.
The Telegraph, London; Bloomberg, AP
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