  The local Sugawara constructions of the "small" N=4 SCA in terms of
supercurrents of N=2 extensions of the affinization of the sl(2|1) and sl(3)
algebras are investigated. The associated super mKdV type hierarchies induced
by N=4 SKdV ones are defined. In the sl(3) case the existence of two
inequivalent Sugawara constructions is found. The long one involves all the
affine sl(3)-valued currents, while the "short" one deals only with those from
the subalgebra sl(2)\oplus u(1). As a consequence, the sl(3)-valued affine
superfields carry two inequivalent mKdV type super hierarchies induced by the
correspondence between "small" N=4 SCA and N=4 SKdV hierarchy. However, only
the first hierarchy posseses genuine global N=4 supersymmetry. We discuss
peculiarities of the realization of this N=4 supersymmetry on the affine
supercurrents.
