  We show that $QCD_2$ with adjoint fermions involves instantons due to
nontrivial $\pi_1[SU(N)/Z_N]~=~Z_N$. At high temperatures, quasiclassical
approximation works and the action and the form of effective (with account of
quantum corrections) instanton solution can be evaluated. Instanton presents a
localized configuration with the size $\propto g^{-1}$. At $N=2$, it involves
exactly 2 zero fermion modes and gives rise to fermion condensate
$<\bar{\lambda}^a \lambda^a>_T$ which falls off $\propto \exp\{-\pi^{3/2}
T/g\}$ at high $T$ but remains finite.
  At low temperatures, both instanton and bosonization arguments also exhibit
the appearance of fermion condensate $<\bar{\lambda}^a \lambda^a>_{T=0} ~\sim
~g$. For $N>2$, the situation is paradoxical. There are $2(N-1)$ fermion zero
modes in the instanton background which implies the absence of the condensate
in the massless limit. From the other hand, bosonization arguments suggest the
appearance of the condensate for any $N$. Possible ways to resolve this paradox
(which occurs also in some 4-dim gauge theories) are discussed.
