  We discuss two classes of exact (in $\a'$) string solutions described by
conformal sigma models. They can be viewed as two possibilities of constructing
a conformal model out of the non-conformal one based on the metric of a
$D$-dimensional homogeneous $G/H$ space. The first possibility is to introduce
two extra dimensions (one space-like and one time-like) and to impose the null
Killing symmetry condition on the resulting $2+D$ dimensional metric. In the
case when the ``transverse" model is $n=2$ supersymmetric and the $G/H$ space
is K\"ahler-Einstein the resulting metric-dilaton background can be found
explicitly. The second possibility - which is realised in the sigma models
corresponding to $G/H$ conformal theories - is to deform the metric,
introducing at the same time a non-trivial dilaton and antisymmetric tensor
backgrounds. The expressions for the metric and dilaton in this case are
derived using the operator approach in which one identifies the equations for
marginal operators of conformal theory with the linearised (near a background)
expressions for the `$\b$-functions'. Equivalent results are then reproduced in
the direct field-theoretical approach based on computing first the effective
action of the $G/H$ gauged WZW model and then solving for the $2d$ gauge field.
Both the bosonic and the supersymmetric cases are discussed. ( To be published
in the Proceedings of the 26 Workshop ``From Superstrings to Supergravity",
Erice, 5-12 December,1992.)
