will Shimano Shimano Dura Ace 7700 STI Flight Deck work with Rear Derailleur Shimano XT RD-M771
Yes, all nominally 9-speed Shimano mountain RDs will work with ST-7700, and all pre-11-speed road FDs will work with ST-7703, except for FD-4700 at present and any future 10-or-fewer groups that use the 11-speed actuation ratio.