  The B-RNS-GSS formalism containing both RNS and GS worldsheet variables is
extended for the description of the Type II superstring in curved backgrounds.
The BRST charge of the theory is expressed in terms of $N=(1,1)$ superconformal
generators $(T,G; {\widehat{T}}, {\widehat{G}})$, and the classical
anticommutation relations $\{G,G\}=-2T$ and
$\{{\widehat{G}},{\widehat{G}}\}=-2{\widehat{T}}$ are shown to imply the Type
II supergravity equations of motion. The particular case of the Type IIB
superstring in an $AdS_5\times S^5$ background is discussed and shown to be
classically integrable.
