The spin dependent deuteron structure functions are investigated in the relativistic model of deuteron. It is shown that the deuteron structure function g 2 (X) can be considered properly only in the in nite momentum frame where the virtual photon has pure transverse components (q 0 = q 3 ! 0 at P ! 1), whereas in the conventional Breit frame the impulse approximation for g 2 (X) may be violated due to q q pair creation by the virtual photon. It is shown that due to relativistic e ects the deuteron structure function g 2 (X) has a nontrivial contribution determined by rst derivative of the nucleon structure function g 1 (x).Such contribution is small but it increases when X ! 1. It may achieve about 10 % at X 0:75 and could be essentially larger for the transverse structure function g ? (X):