Abstract. The possibility and conditions for generation of the correlated signals of cluster superfluorescence (CSF) under two and three-quantum excitation of nanostructured samples CdSe/CdS by two crossed at the angle of 60° femtosecond beams of the Ti:Sapphire laser radiation are investigated. It is shown that intensity of the CSF signals is proportional to the cube of the number of clusters and that these collective signals are generated in mutually opposite directions k1 -k2 and k2 -k1, where k1, k2 are the wavevectors of the exciting pulses.R. Dicke in his basic work [1] devoted to the optical superradiance (SR) also discussed the case of an incoherent pump when at the initial moment of time the radiators (atoms, molecules or clusters) are in the excited state and have no macroscopic polarization. It was shown that under conditions when the linear dimensions of the system are much less than the wavelength of the radiated light such a system of the inverted atoms can spontaneously undergo transition to the ground-state during the time which is inversely proportional to the number of atoms N. This case of the spontaneous collective radiation was named in [2] as a superfluorescence (SF). The SF, as well as the SR, is a perfect example of a self-organization [3]. The collective character of photon emission in the SF is due to the indistinguishability of atoms in a system (with linear dimensions L < λ) interacting with a field. The SF signals appear to be delayed by the time 0 The samples studied in the present work are composites consisting of the CdSe/CdS nanoparticles (of core/shell type) dispersed into a PMMA polymer matrix. The average size of grown particles with the spherical or elliptical shape is equal to 510 -7 cm. The wavelength of the Ti:Sapphire laser is equal to 810 -5 cm with pulse duration of 40 fs. So, the area of excitation with the linear dimensions of 810 -5 cm can involve about 160 areas (clusters) emitting the SF signal. For the first time the term "cluster superfluorescence" appeared in paper [4] while studying the quadrupole superradiance [5,6]. The authors of this paper constructed the generalized Dicke model and showed that the intensity I of the quadrupole cluster superradiation is proportional to N 3 . In our case, the situation is more complicated because of the two-and three-photon modes of the excitation by crossed femtosecond laser