  We discuss solutions of the heterotic string theory which are analogous to
bosonic and superstring backgrounds related to coset conformal field theories.
A class of exact `left-right symmetric' solutions is obtained by supplementing
the metric, antisymmetric tensor and dilaton of the superstring solutions by
the gauge field background equal to the generalised Lorentz connection with
torsion. As in the superstring case, these backgrounds are $\a'$-independent,
i.e. have a `semiclassical' form. The corresponding heterotic string sigma
model is obtained from the combination of the (1,0) supersymmetric gauged WZNW
action with the action of internal fermions coupled to the target space gauge
field. The pure (1,0) supersymmetric gauged WZNW theory is anomalous and does
not describe a consistent heterotic string solution. We also find (to the order
$\alpha'^3$) a two-dimensional perturbative heterotic string solution with the
trivial gauge field background. To the leading order in $\alpha'$ it coincides
with the known $SL(2,R)/U(1)$ bosonic or superstring solutions. This solution
does not correspond to a `heterotic' combination of the left superstring and
right bosonic $L_0$-operators at the conformal field theory level. Some duality
properties of the heterotic string solutions are studied.
