  We compute the operator which creates the missing degenerate states in the
algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to
the concept of an elliptic current operator. We find that in sharp contrast
with the corresponding formalism in the six-vertex model at roots of unity the
current operator is not nilpotent with the consequence that in the construction
of degenerate eigenstates of the transfer matrix an arbitrary number of exact
strings can be added to the set of regular Bethe roots. Thus the original set
of free parameters {s,t} of an eigenvector of T is enlarged to become
{s,t,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers
\lambda_{c,j} and arbitrary n.
