A model with anomalous occupancy is applied to Hg-based cuprate superc
onductors. The anomaly consists of a small energy gap near the Fermi s
urface, the scale of the gap anomaly is of order of the cutoff (v.g. D
ebye) energy. Values of the anomalous occupancy parameters for Hg-base
d superconductors are obtained for different values of the ratio R and
the effective coupling constant, within the weak coupling. As these m
aterials have the highest transition temperature known for layered cop
per-oxide superconductors, they serve as a new testing ground for vari
ous proposed models.