  Space-time N=2 and N=4 superconformal algebras can be built using world-sheet
free fields or, equivalently, free field representations of osp(1|2) and
sl(2|1), respectively. A prescription for the calculation of space-time
correlators is given. As applications we compute one and two-point correlation
functions of Virasoro (superVirasoro) generators. We also present a possible
scenario for taking into account of NS fivebranes in the framework of our
construction for description of superstring on AdS_3. It is nothing but a
simplified version of Green's ``world-sheets for world-sheets''.
