We report a combined experimental and theoretical study of the two-photon absorption and excited emission properties of monodisperse ligand stabilized Ag₁₁ , Ag₁₅ and Ag₃₁ nanoclusters in aqueous solutions. The nanoclusters were synthesized using a cyclic reduction under oxidative conditions and separated by vertical gel electrophoresis. The two-photon absorption cross-sections of these protected noble metal nanoclusters measured within the biologically attractive 750-900 nm window are several orders of magnitude larger than that reported for commercially available standard organic dyes. The two-photon excited fluorescence spectra are also presented for excitation wavelengths within the same excitation spectral window. They exhibit size-tunability. Because the fundamental photophysical mechanisms underlying these multiphoton processes in ligand protected clusters with only a few metal atoms are not fully understood yet, a theoretical model is proposed to identify the key driving elements. Elements that regulate the dipole moments and the nonlinear optical properties are the nanocluster size, its structure and the charge distribution on both the metal core and the bound ligands. We coined this new class of NLO materials as "Ligand-Core" NLO-phores.