We present a manifestly N = 2 supersymmetric formulation of N = 2 supe
r-W-3((2)) algebra (its classical version) in terms of the spin-one un
constrained supercurrent generating an N = 2 superconformal subalgebra
and the spins-1/2, two bosonic and spins-1/2, two fermionic constrain
ed supercurrents. We consider a superfield reduction of N = 2 superW(3
)((2)) to N = 2 super-W-3 and construct a family of evolution equation
s for which N = 2 super-W-3((2)) provides the second Hamiltonian struc
ture.