The spin-freezing process in underdoped cuprate superconductors, observed most by NMR-NQR relaxation and muon spin rotation and sometimes interpreted as coexistence of antiferromagnetic and superconducting states, 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 magnetic fields caused by sliding motions of orbital currents coexisting with d-wave superconducting state. A direct explanation of the experimental results, in underdoped Y2-xCaxBa2Cu3O6.1 and La2-xSrxCuO4, is thus given in terms of freezing of orbital current fluctuations, and mean squared amplitudes of the related internal magnetic fields are estimated.