The superconducting penetration depth lambda(T) has been measured in RFeAsO(0.9)F(0.1) (R = La, Nd) single crystals (R-1111). In Nd-1111, we find an upturn in lambda(T) upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, Deltalambda_{L}(T) proportional, variantT;{2} at low temperatures. The same T2 variation of lambda(T) was found in nonmagnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth anisotropy over the full temperature range is consistent with two-gap superconductivity. Based on this and on our previous work, we conclude that both the RFeAsO (1111) and BaFe(2)As(2) (122) families of pnictide superconductors exhibit unconventional two-gap superconductivity.