We report the transverse relaxation rates 1/T2's of the 63 Cu nuclear spin-echo envelope for doublelayer high-Tc cuprate superconductors HgBa2CaCu2O 6+δ from underdoped to overdoped. The relaxation rate 1/T2L of the exponential function (Lorentzian component) shows a peak at 220−240 K in the underdoped (Tc = 103 K) and the optimally doped (Tc = 127 K) samples but no peak in the overdoped (Tc = 93 K) sample. The enhancement in 1/T2L suggests development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden in the pseudogap states.