  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 $T_c$ 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
spin-lattice 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 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 symmetry axis of the electric field gradient tensor
with magnitudes of the order of 1000 G. We also discuss the possible
microscopic origin of the observed internal magnetic fields.
