  We investigate the long-distance asymptotic behavior of the dimer
correlations in the spin-1/2 alternating $XY$chain both at T=0 and at
sufficiently low-temperatures. The correlations consist of the dimer long-range
order part and the exponentially decaying one. Although the dimer long-range
order takes the different values depending on the choice of the spin pairs, the
behavior in the decaying term is same irrespective of the choice of spin pairs.
