  We construct the nonlinear $N=2$ super-$W_3^{(2)}$ algebra with an arbitrary
central charge at the classical level in the framework of Polyakov "soldering"
procedure. It contains two non-intersecting subalgebras: $N=2$ superconformal
algebra and $W_3^{(2)}$ and their closure gives the $N=2$ super-$W_3^{(2)}$
algebra. Besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras,
it comprises two pairs of fermionic currents with spins 1 and 2. The hybrid
field realization and contractions to the zero central charge are constructed.
