The effect of aluminum and silicon as micro-alloying elements in TX32 magnesium alloy on its hot deformation behavior has been studied by conducting uniaxial compression tests at various combinations of temperatures and strain rates in the ranges 300-500°C and 0.0003-10 s^-1. A processing map has been developed and the effect of processing conditions on deformation behavior has been analyzed. Two processing windows that enable good hot working of the alloy are identified at (1) 390-500°C/0.0003-0.005 s^-1 (Domain 1), (2) 430-500°C/0.3-10 s^-1 (Domain 2). The kinetic analysis is obeyed in these two domains and the relevant apparent activation energy values are found to be 215 and 170 kJ/mole respectively. These are higher than that for self-diffusion in magnesium suggesting that intermetallic particles present in the matrix generate back stress.