  An infinite series of Grassmann-odd and Grassmann-even flow equations is
defined for a class of supersymmetric integrable hierarchies associated with
loop superalgebras. All these flows commute with the mutually commuting bosonic
ones originally considered to define these hierarchies and, hence, provide
extra fermionic and bosonic symmetries that include the built-in N=1
supersymmetry transformation. The corresponding non-local conserved quantities
are also constructed. As an example, the particular case of the principal
supersymmetric hierarchies associated with the affine superalgebras with a
fermionic simple root system is discussed in detail.
