  Kinnersley--type representation is constructed for the four--dimensional
Einstein--Maxwell--dilaton--axion system restricted to space--times possessing
two non--null commuting Killing symmetries. New representation essentially uses
the matrix--valued $SL(2,R)$ formulation and effectively reduces the
construction of the Geroch group to the corresponding problem for the vacuum
Einstein equations. An infinite hierarchy of potentials is introduced in terms
of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of
Kinnersley--Chitre known for the vacuum Einstein equations.
