We report $^{75}$As nuclear quadrupole resonance (NQR) studies on superconducting oxypnictide LaFeAsO$_{0.92}$F$_{0.08}$ ($T_{rm c}$ = 23 K). The temperature dependence of the spin lattice relaxation rate (1/$T_1$) decreases below $T_{rm c}$ without a coherence (Hebel-Slichter) peak and shows a temperature dependence that is not simple power-law nor exponential. We show that the result can be understood in terms of two superconducting gaps of either $d$- or ${pm}s$-wave symmetry, with the larger gap $Delta_1sim 4 k_{rm B}T_{rm c}$ and the smaller one $Delta_2 sim 1.5 k_{rm B}T_{rm c}$. Our result suggests that the multiple-gaps feature is universal in the oxypnictides superconductors, which is probably associated with the multiple electronic bands structure in this new class of materials. We also find that 1/$T_1T$ above $T_{rm c}$ increases with decreasing temperature, which suggests weak magnetic fluctuations in the normal state.
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