  We demonstrate that the $\tau^{(j)}$-matrices in the superintegrable chiral
Potts model possess the Onsager algebra symmetry for their degenerate
eigenvalues. The Fabricius-McCoy comparison of functional relations of the
eight-vertex model for roots of unity and the superintegrable chiral Potts
model has been carefully analyzed by identifying equivalent terms in the
corresponding equations, by which we extract the conjectured relation of
$Q$-operators and all fusion matrices in the eight-vertex model corresponding
to the $T\hat{T}$-relation in the chiral Potts model.
