  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 infinite momentum
frame where the virtual photon has pure transverse components
($q_{0}=-q_{3}\rightarrow 0$ at $ P\rightarrow \infty $), whereas in the
conventional Breit frame the impulse approximation for $g_{2}(X)$ may be
violated due to $q\bar{q}$ pair creation by the virtual photon. It is shown
that due to relativistic effects the deuteron structure function $g_{2}(X)$ has
a nontrivial contribution determined by first derivative of the nucleon
structure function $g_{1}(x)$. Such contribution is small but it increases when
$X \rightarrow 1$. It may achieve about 10 \% at $ X \sim 0.75$ and could be
essentially larger for the transverse structure function $g_{\perp}(X).$
