  The two-dimensional manifestly locally supersymmetric actions describing the
N=2 and N=4 extended super-Liouville theory coupled to the N=2 and N=4
conformal supergravity, respectively, are constructed in superspace. It is
shown that the N=4 super-Liouville multiplet is described by the improved
twisted-II scalar multiplet TM-II, whose kinetic terms are given by the
SU(2)xU(1) WZNW model.
