  We report the transverse relaxation rates 1/$T_2$'s of the $^{63}$Cu nuclear
spin-echo envelope for double-layer high-$T_c$ cuprate superconductors
HgBa$_{2}$CaCu$_{2}$O$_{6+d}$ from underdoped to overdoped. The relaxation rate
1/$T_{2L}$ of the exponential function (Lorentzian component) shows a peak at
220$-$240 K in the underdoped ($T_c$ = 103 K) and the optimally doped ($T_c$ =
127 K) samples but no peak in the overdoped ($T_c$ = 93 K) sample. The
enhancement in 1/$T_{2L}$ suggests development of the zero frequency components
of local field fluctuations. Ultraslow fluctuations are hidden in the pseudogap
states.
