We report pure zero field nuclear magnetic resonance (NQR) measurements on the optimally doped three layer high-T c -compounds HgBaCaCuO and HgBaCaCuO(F) with T c ¼ 134 K. Above T c two Cu NQR line pairs are observed in the spectra corresponding to the two inequivalent Cu lattice sites. Below T c the Cu NQR spectra show additional lines leading to the extreme broadened Cu NQR spectra at 4.2 K well known for the HgBaCaCuO compounds. The spinlattice relaxation curves follow a triple exponential function with coefficients depend onto the saturation time (number of saturation pulses), whereas the spin-spin relaxation curve is described by a single exponential function. From the spin-lattice relaxation we deduced a complete removal of the Kramers degeneracy of the Cu quadrupole levels indicating that the additional lines are due to a Zeemann splitting of the 63=65 Cu lines due to the spontaneous formation of magnetic moments within the CuO layers. Below 140 K, the spectra are well fitted by a number of 6 63=65 Cu line pairs. From the number of the Cu lines, the position of the lines relative to each other and the complete removal of the Kramers degeneracy we deduced an orientation of the magnetic moments parallel to the c-axis with magnitudes of the order of 1000 G. We also discuss the possible microscopic origin of the observed internal magnetic fields.