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Three terrorism suspects were involved in a plot to behead a member of the British public "imminently" when they were arrested, a court has heard.
Nadir Ali Sayed, Yousaf Shah Syed and Haseeb Hamayoon were arrested three days before Remembrance Sunday.
During a preliminary hearing at Westminster Magistrates' Court, none of them applied for bail and they were remanded in custody.
Full details of the alleged plot were not given.
Rebecca Mundy, prosecuting, said the charges related to an alleged plan to carry out a beheading.
Mr Sayed, 21, from Hounslow, Mr Syed, 19, from High Wycombe, and Mr Hamayoon, 27, from Hayes, were arrested on 6 November in London and High Wycombe.
A fourth man, arrested in Uxbridge, west London, was released on Saturday with no further action against him.
The trio were charged earlier on Thursday - the 14th and final day that they could be held by police under terrorism legislation.
BBC home affairs correspondent Danny Shaw said Mr Sayed and Mr Syed stood in the dock for most of the proceedings, "smiling and laughing as details were read out", while Mr Hamayoon remained seated.
Scotland Yard said the men had been charged with being "jointly engaged" in preparing for committing acts of terrorism.