  A complete, gauge-invariant computation of two loop virtual corrections
involving closed fermion loops to the polarized M{\o}ller scattering asymmetry
is presented. The set of contributions involving two closed fermion loops and
the set involving one closed fermion loop are numerically similar in magnitude
to the one-loop bosonic corrections and yield an overall correction of 1.3%
relative to the tree-level asymmetry. We estimate sizes of remaining two-loop
contributions and discuss implications for the upcoming MOLLER experiment.
