The relaxation and phase transition behaviors of rare-earth ion substituted fast oxide-ion conductors (La1-xRex)2Mo2O9 (Re=Nd, Gd) were investigated by internal friction (IF) measurement in the temperature range 300 K - 950 K. Three different IF peaks (labeled as PL, PH, and PG, respectively) were observed in the rare-earth ion doped La2Mo2O9 samples. Peak PL corresponds to short diffusion processes of oxygen ions among different oxygen vacancy sites. Peak PH is associated with the static/dynamic disorder transition in oxygen ion distribution. Peak PG is a newly discovered peak embodying phase transition-like characteristics and is suggested to be related to order-disorder transition associated with the rearrangement of La/ Re sub-lattice.