  We study the possibility to establish $L$-operator's formalism by
Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky (FRST) for quantized current
algebras, that is, for quantum affine algebras in the ''new realization '' by
V. Drinfeld with the corresponding Hopf algebra structure and for their Yangian
counterpart. We establish this formalism using the twisting procedure by
Tolstoy and the second author and explain the problems which FRST approach
encounter for quantized current algebras. We show also that, for the case of
$U_q(\hat {\frak sl}_n)$, entries of the L-operators of FRTS type give the
Drinfeld current operators for the non-simple roots, which we discovered
recently. As an application we deduce the commutation relations between these
current operators for $U_q(\hat {\frak sl}_3)$.
