Abstract :
The two-dimensional (2D) 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) ⊗ U(1) WZNW model.
