  The letter deals with the spin-freezing process observed by means of NMR-NQR
relaxation or by muon spin rotation in underdoped cuprate superconductors. This
phenomenon, sometimes referred as coexistence of antiferromagnetic and
superconducting order parameters, is generally thought to result from randomly
distributed magnetic moments related to charge inhomogeneities (possibly
stripes) which exhibit slowing down of their fluctuations on cooling below
T$_c$ . Instead, we describe the experimental findings as due to fluctuating,
vortex-antivortex, orbital currents state coexisting with d-wave
superconducting state. A direct explanation of the experimental results, in
underdoped Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{6.1}$ and La$_{2-x}$Sr$%_x$CuO$_4$,
is thus given in terms of freezing of orbital current fluctuations.
