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A deep understanding of the character of superconductivity in the recentlydiscovered Fe-based oxypnictides ReFeAsO1-xFx (Re = rare-earth) necessarilyrequires the determination of the number of the gaps and their symmetry in kspace, which are fundamental ingredients of any model for the pairing mechanismin these new superconductors. In the present paper, we show that point-contactAndreev-reflection experiments performed on LaFeAsO1-xFx (La-1111) polycrystalswith Tc ~ 27 K and SmFeAsO0.8F0.2 (Sm-1111) ones with Tc ~ 53 K gavedifferential conductance curves exhibiting two peaks at low bias and twoadditional structures (peaks or shoulders) at higher bias, an experimentalsituation quite similar to that observed by the same technique in pure anddoped MgB2. The single-band Blonder-Tinkham-Klapwijk model is totally unable toproperly fit the conductance curves, while the two-gap one accounts remarkablywell for the shape of the whole experimental dI/dV vs. V curves. These resultsgive direct evidence of two nodeless gaps in the superconducting state ofReFeAsO1-xFx (Re = La, Sm): a small gap, Delta1, smaller than the BCS value(2Delta1/kBTc ~ 2.2 - 3.2) and a much larger gap Delta2 which gives a ratio2Delta2/kBTc ~ 6.5 - 9. In Sm-1111 both gaps close at the same temperature,very similar to the bulk Tc, and follow a BCS-like behaviour, while in La-1111the situation is more complex, the temperature dependence of the gaps showingremarkable deviations from the BCS behaviour at T close to Tc. The normal-stateconductance reproducibly shows an unusual, but different, shape in La-1111 andSm-1111 with a depression or a hump at zero bias, respectively. Thesestructures survive up to T* ~ 140 K, close to the temperatures at whichstructural and magnetic transitions occur in the parent, undoped compound.

Point-contact Andreev-reflection spectroscopy in ReFeAsO_{1-x}F_x (Re = La, Sm): Possible evidence for two nodeless gaps