The group want former chairman Malcolm Murray and ex-director Paul Murray made directors at Ibrox again and for them to be joined on the board by Scott Murdoch and Alex Wilson.
Malcolm Murray, Paul Murray and other shareholders Ian Cormack, John Graham and Colin Howell maintain that because of Rangers' failure proper notice will not be given of the AGM and the resolutions for the directors' appointment will not form part of the business for the meeting scheduled for October 24.
Their counsel Richard Keen QC told Lord Kinclaven that notice of the AGM only appeared on a Rangers website on Thursday.
The Court of Session in Edinburgh heard that notice of it would have to be given by October 2.
But Heriot Currie QC, for Rangers, said that notice of the AGM had been made both by hard copy and through a website in accordance with companies legislation.
He said: "We have information from a third party explaining that the relevant notice was on the website at 9am on October 1."
But Mr Keen, Dean of Faculty of Advocates, maintained that it was not the formal notice, but a regulatory notice.
He said: "It is not the case that notice of the AGM went on the website on October 21 as documents suggest."
The shareholders said in their action that on September 27 they each made a request in writing to Rangers of four resolutions it was intended to move at the AGM to appoint the Murrays, Mr Murdoch and Mr Wilson to the board.
Paul Murray said: "We are delighted with the hearing and we look forward to having the opportunity of establishing the validity of our proposed director nominations at the full hearing.
"In the meantime we would ask shareholders to do nothing until it is clear what they are being asked to vote upon."