  We construct N=2 affine current algebras for the superalgebras
sl(n|n-1)^{(1)} in terms of N=2 supercurrents subjected to nonlinear
constraints and discuss the general procedure of the hamiltonian reduction in
N=2 superspace at the classical level. We consider in detail the simplest case
of N=2 sl(2|1)^{(1)} and show how N=2 superconformal algebra in N=2 superspace
follows via the hamiltonian reduction. Applying the hamiltonian reduction to
the case of N=2 sl(3|2)^{(1)}, we find two new extended N=2 superconformal
algebras in a manifestly supersymmetric N=2 superfield form. Decoupling of four
component currents of dimension 1/2 in them yields, respectively, u(2|1) and
u(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how the N=2
superfield formulations of N=2 W_{3} and N=2 W_{3}^{(2)} superconformal
algebras come out in this framework, as well as some unusual extended N=2
superconformal algebras containing constrained N=2 stress tensor and/or spin 0
supercurrents.
