The six independent elastic constants of a gamma-TiAl (Ti44Al56) single crystal have been measured for the first time from room temperature to 750 K using a resonant ultrasound spectroscopy technique. The values of C-12 and C-13 are virtually temperature independent, whereas C-11, C-33, C-44, and C-66 decrease between 6 and 9% from 300 to 750 K, The two independent linear thermal expansion coefficients alpha(1) (along [100] direction) and alpha(2) (along [001] direction) of single crystal gamma-TiAl have been measured from 4 to 750 K using two different apparatus. The elastic constants have been corrected for the effect of thermal expansion, and the corrected C-ij have been used to calculate the Young's and shear moduli along various crystal directions. The elastic constants and moduli values have also been extrapolated to 1273 K. Finally, the elastic anisotropy has also been calculated as a function of temperature. (C) 1997 Elsevier Science S.A.