Lawyers yesterday started to outline details of Liberty's claims against the Government Communications Headquarters (GCHQ), the Secret Intelligence Service - MI6, and the Security Service - MI5, at a special tribunal in London.
The public hearing before the Investigatory Powers Tribunal, which investigates complaints about the conduct of the security and intelligence services and often sits behind closed doors, is expected to end later this week.
Five judges - chaired by tribunal president Mr Justice Burton - are hearing legal argument.
Liberty says there is a "reasonable likelihood" that intelligence services have "interfered with" its private communications in breach of rights to private life and freedom of expression.
Officials want the tribunal to declare that GCHQ, MI6 and MI5 acted unlawfully.
Liberty says its claim is based on intelligence services' use of two computer programmes - PRISM and Tempora. Officials say PRISM is a programme used by the United States National Security Agency (NSA) to obtain data and Tempora a programme apparently used by GCHQ to intercept communications through fibre optic cables entering and leaving the UK.
The case was launched in the wake of revelations by former NSA analyst Edward Snowden.
James Eadie QC, who heads the Government legal team, told judges: "There is a clear need for the intelligence services to be able to share intelligence - on a proportionate basis - with foreign intelligence partners."
The inquiry continues.