United Continental is facing a challenge from two shareholders calling for changes to the airline's board.
Altimeter and PAR said the airline has done little to improve performance and announced they would put forward six new board members for election at United's annual meeting.
They blamed an "entrenched board" on the airline's failure to make progress.
But United's chairman Henry Meyer said the shareholders had ignored attempts the board had made to engage them.
Together Altimeter and PAR control 7.1% of United's shares.
The investors object to United's decision, on Monday, to expand the size of its board with three new members.
"Yesterday's last-ditch effort - adding just three people to its now 15-person board - is a cynical attempt to preserve power by this entrenched board," said Brad Gerstner chief executive of Altimeter.
United announced its chief executive officer Oscar Munoz will return to full time work on 14 March after recovering from a heart attack in October.
"PAR and Altimeter have unilaterally taken this hostile action with no concern that a proxy fight could distract the company from executing on Oscar [Munoz]'s strategic plan," Mr Meyer said.
Among Altimeter's and PAR's nominees for new board members is former Continental Airlines chief executive Gordon Bethune - who ran that airline until 2004.
United and Continental merged in 2010.