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The wavelength dependence of the quadratic hyperpolarizability of 11 nm diam gold nanoparticles, is reported as measured by hyper Rayleigh scattering. An important photoluminescence background underlying the hyper Rayleigh signal is observed, a contribution attributed to radiative electron-hole recombinations following multiphoton excitation favored by adsorbed organic compound like citrate on the surface of the nanoparticles. The absolute value of the quadratic hyperpolarizability of gold spherical nanoparticles is determined and a strong enhancement is observed for harmonic frequencies in resonance with the dipolar surface plasmon excitation. No contribution of the interband transition is observed. The absolute values reported, beta(C)=5.1x10(-26) esu at the second harmonic energy 2.39 eV, have been measured with femtosecond long laser pulse, and are 1 order of magnitude weaker that the one previously reported with nanosecond long pulses. This difference can be related to similar measurements performed on the second order hyperpolarizability of gold nanoparticles and may be attributed to different electronic relaxation regimes. Finally, the spectrum of the quadratic hyperpolarizability is compared to the theoretically expected one., ((c) 2004 American Institute of Physics.)