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Here we present the non-perturbative theory of light-atom interaction suitable to describe the nonlinear atomic response in the case of arbitrary polarized multicolour laser fields. The basic principles of the theory are presented in [A.V Andreev., S.Yu. Stremoukhov, O.A. Shoutova, “Nonlinear Optical Response of an Atom in the Field of Femtosecond Laser Pulses with Near-Atomic Intensity”, JETP Letters, 93( 8), 476 (2011)]. The specific feature of the proposed theory is in the fact that the exact analytical solutions of boundary value problem for an atom in the external field are used to calculate the matrix elements of quantum-mechanical operators. The most important advantage of this approach lies in the account of difference in the symmetry properties of “free atom” and “an atom in the external field” problems. The obtained results show that in the case of the two-color laser field the HHG spectra strongly depend on the parameters of irradiating pulses. The main control parameters are: (a) the relative orientation of polarization vectors of linear polarized laser pulses at basic frequency and second harmonic; (b) the delay time between pulses: (c) the pulse temporal widths, (d) their in-tensities and (e) chirp of the laser field components. The influence of these parameters on the emission spectra is illustrated and discussed.