  The construction of Miura and B\"acklund transformations for $A_n$ mKdV and
KdV hierarchies are presented in terms of gauge transformations acting upon the
zero curvature representation. As in the well known $sl(2)$ case, we derive and
relate the equations of motion for the two hierarchies. Moreover, the
Miura-gauge transformation is not unique, instead, it is shown to be connected
to a set of generators labeled by the exponents of $A_n$ The construction of
generalized gauge-B\"acklund transformation for the $A_n$-KdV hierarchy is
obtained as a composition of Miura and B\"acklund-gauge transformations for
$A_n$-mKdV hierarchy. The zero curvature representation provide a framework
which is universal within all flows and generate systematically B\"acklund
transformations for the entirely hierarchy.
