  We present a manifestly $N=2$ supersymmetric formulation of $N=2$
super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1
unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the
spins 1/2, 2 bosonic and spins 1/2, 2 fermionic constrained supercurrents. We
consider a superfield reduction of $N=2$ super-$W_3^{(2)}$ to $N=2$ super-$W_3$
and construct a family of evolution equations for which $N=2$ super-$W_3^{(2)}$
provides the second hamiltonian structure.
