The nonlocal conservation laws for the N = 1 supersymmetric KdV equati
on are shown to be related in a simple way to powers of the fourth roo
t of its Lax operator. This provides a direct link between the supersy
mmetry invariance and the existence of nonlocal conservation laws. It
is also shown that nonlocal conservation laws exist for the two integr
able N = 2 supersymmetric KdV equations whose recursion operator is kn
own.