The γ-TiAl intermetallic compound with suitable alloying additions has shown considerable promise as a material for high-temperature applications. Diffusion studies in this alloy system are useful in assessment of their creep behaviour and structural stability in service conditions. Tracer diffusion coefficients of 51Cr and 54Mn in a γ-TiAl intermetallic compound containing 54.1 at. % aluminium were determined in the temperature range from 1095 to 1470 K. The temperature dependence of both the diffusing species follows a linear Arrhenius behaviour and can be expressed as DCr= 4.4 x 10_3exp(-350 kJ mol-1/RT)m2 s-1 and DMn = 1.2 x 10-3 x exp(-326 kJ mol-1/RT)m2 s-1. The data are analysed on the basis of empirical correlations between the diffusion and melting parameters applicable for conventional mono-vacancy diffusion mechanism in metals. It is concluded that impurity diffusion in γ-TiAl occurs through the migration of thermal vacancies via nearest-neighbour or next-nearest neighbour jumps.