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We study collision of two atoms with formation of Feshbach resonance atcombined interaction with the external magnetic field and laser radiation. Incases of one- and two-photon resonances of laser radiation with two discretevibrational molecular levels, we show that Feshbach resonances appear atinteraction of external magnetic field with dressed states formed viaAutler-Townes effect. In addition, in case of one-photon resonance the lowervibrational molecular state is coupled by laser radiation with the continuum ofthe elastic channel and forms laser-induced Feshbach resonance via bothAutler-Townes effect and LICS mechanism. We study the combined process offormation of Feshbach resonances; this enables the control of Feshbachresonance by varying the magnetic field and intensity and frequency of laserradiation. We obtain the cross-sections of elastic and inelastic scattering andshow that quenching of resonance occurs at the energy equal to that of thesystems ground state. Dependence of the cross-sections on the magnetic fieldand laser intensity is examined in detail. In all considered cases, thescattering length is obtained depending on the magnetic and laser fields arestudied. In the absence of magnetic interaction if the hyperfine substates ofthe quasibound state in the closed channel and those of individual collidingatoms in the open channel are the same, Feshbach resonances may arise via weakinteraction between nuclear and electronic motions, which leads to transitionsbetween electronic states. The obtained results can be employed in new studiesof collisions of cold atoms, e.g., of alkali metal atoms and for interpretationof new experiments in BECs.

Influence of external magnetic and laser radiation fields on Feshbach resonances in collision of atoms