In this paper, the influence of solvents on the first hyperpolarizability beta of nonlinear optical (NLO) molecules is studied at 25 degrees C for solutions of p-nitroaniline and N,N-dimethyl paranitroaniline in some 50 solvents belonging to different classes. The hyperpolarizabilities deduced from measured hyper-Rayleigh scattering are the relative ones with as reference that of paranitroaniline in 1,4-dioxane. Taking for the latter the literature value of 16.9 10(-30) esu, the beta values vary from 14.4 to 29.9 10(-30) esu for paranitroaniline and from 28.7 to 46.2 10(-30) esu for N,N-dimethyl paranitroaniline. A selection of the solvents is made on the basis of the fraction of the time gamma(0) during which the NLO molecule is not involved in H-bonding with the solvent molecules. gamma(0) can be determined from the solubility in the given solvent. The formation of specific solute-solvent interactions as H-bonds always increases the hyperpolarizability beta. In the absence of such interactions, the hyperpolarizability increases with the square root of the gaseous dipole moment of the solvent molecule and decreases when the mean interdistance between the center of the NLO molecule and the closest solvent dipole increases. A statistical study of a large number of solvents leads indeed to the correlation beta = beta(gas) + a root mu(S)/V-S where a is a constant fora given NLO molecule, When H-bonds are formed the correlation becomes : beta = beta(gas) + gamma(0)a root mu(S)/V-S + (1 - gamma(0))b root mu(S), where b is a constant for a given NLO molecule. H-bond formation enhances the hyperpolarizability because it reduces the distance between the neighboring solvent dipole and the center of the NLO molecule to a constant value, independent of V-S.