  We study the sum rules of double Gamow-Teller (DGT) excitations through
double spin-isospin operator $(\sigma t_-)^2$. In general, $2^+$ states in the
granddaughter nuclei have dominant transition strength in DGT excitations and
$0^+$ states are weak, except in $T=1$ mother nuclei in which $0^+$ strength is
competitive with 2$^+$ strength. The isospin selection of DGT is also discussed
among 5 possible isospin states in granddaughter nuclei. A possibility to
extract the unit cross section for the DGT transition strength is pointed out
in the $(\sigma t_-)^2$ excitation of double isobaric analog state (DIAS) in
$T=1$ nuclei.
