  A Yang-Baxter relation-based formalism for generalized quantum affine
algebras with the structure of an infinite Hopf family of (super-) algebras is
proposed. The structure of the infinite Hopf family is given explicitly on the
level of $L$ matrices. The relation with the Drinfeld current realization is
established in the case of $4\times4$ $R$-matrices by studying the analogue of
the Ding-Frenkel theorem. By use of the concept of algebra ``comorphisms''
(which generalize the notion of algebra comodules for standard Hopf algebras),
a possible way of constructing infinitely many commuting operators out of the
generalized $RLL$ algebras is given. Finally some examples of the generalized
$RLL$ algebras are briefly discussed.
