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Single-walled carbon nanotubes (SWNT) are one-dimensional nanostructures where the Coulomb interactions between charge carriers are strongly enhanced compared to systems of higher dimensionality. This results in an electron-hole bound state -the so-called exciton- with a binding energy of the order of one third of the bandgap, which controls the SWNTs optical properties. As a matter of fact, the exciton-exciton interactions are particularly efficient and drive the exciton recombination and dephasing dynamics [1-3]. The investigation of excitonic complexes in semiconducting SWNTs is currently a topic of intense debate. The biexciton and the trion are expected to have a binding energy of about a hundred meVs. Whereas the trion has been recently observed, first in doped nanotubes [4] and then by means of all-optical generation [5], there has been no experimental evidence for the biexciton. In this talk I will present our recent work reporting the observation of the biexciton in semiconducting single-wall carbon nanotubes using nonlinear optical spectroscopy [6]. Our experiments consist in a spectrally resolved pump-probe technique in SWNTs embedded in a gelatine at cryogenic temperature. Our measurements of the differential transmission spectrum reveal the universal asymmetric line shape of the Fano resonance intrinsic to the biexciton transition. For nanotubes of the (9,7) chirality, we find a biexciton binding energy of 106 meV. From the calculation of the nonlinear response, we provide a quantitative interpretation of our measurements, leading to an estimation of the characteristic Fano factor q of 7±3 . This value allows us to extract the first experimental information on the biexciton stability and we obtain a biexciton annihilation rate comparable to the exciton-exciton annihilation one.