  NQR 139La and 63Cu spin-lattice relaxation rate (1/T_1) measurements in a
La1.94Sr0.06CuO4 single crystal are described. Slowing-down of Cu2+ spin
fluctuations is evidenced through a dramatic increase of 139La 1/T_1 on
cooling. While the onset of diamagnetism occurs at Tc=8 K, 1/^{139}T_1 has a
peak at Tg~5 K, when the characteristic frequency of magnetic fluctuations
reaches the NQR frequency nu_Q~19 MHz. In agreement with a number of previous
studies, these results show that the so-called "cluster spin-glass" phase
persists in the superconducting regime. Issues concerning the coexistence of
the two phases are discussed.
