Substantial progress has been achieved in recent years in the experimental and theoretical investigation of the properties of atomic Bose–Einstein condensates. Currently, studies of the dynamics of coupled atomic–molecular condensates under conditions of Feshbach resonance or stimulated photoassociation of two atoms into a molecule are of special interest. It is well–known [1] that the dynamics of wave function BEC can be described by the Gross-Pitaevsky equation, which includes also terms of interparticle interaction. The aim of this work is to explore the effect of self-trapping of the system in the process of stimulated Raman atom–molecule conversion with the formation homonuclear molecule as a single one-step process. We will study three–level energetic Λ –scheme. One of the levels corresponds to the basic condition of two free atoms with energy 2ω0 , and the other – to basic condition of molecule with energy Ω0 . The third level corresponds to activated condition of molecule . The appearance of molecule from two atoms leads to absorption of light quantum with the energy 1 ω and radiation of light quantumω2 . We use Hamiltonian of interaction Hint , describing the effect of induced Raman atomic–molecular conversion as a single process under the influence of two short pulses of resonance laser radiation [2] taking into account the processes of elastic interparticle interaction ( ) ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ, 2 ˆ ˆ ˆ ˆ 1 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1 int 1 2 1 2 1 2 H = g aab+c c + a+a+bc+c + ν a+a+aa + ν b+b+bb + νa+ab+b where aˆ and bˆ are the boson operators of destruction of atoms and molecules, cˆ1 and cˆ2 are the operators of destruction of photons with frequency 1 ω and 2 ω , g is the constant of atomic– molecular conversion, and 1 ν , 2 ν , ν are the constants of interatomic, intermolecular and atom– molecular interactions. Introducing the particle densities , 2 n = a 2 N = b , 2 f1,2 = c1,2 and two components of “polarization” ( ) 1 2 1 2 Q = i aab∗c c∗ − a∗a∗bc∗c and 1 2 1 2 R = aab∗c c∗ + a∗a∗bc∗c , we obtain the system of nonlinear equations ( (2 ) (2 ) ) 2 ((4 ) ( )), 1 2 1 2 2 1 Q = Δ + ν −ν n + ν −ν N R + gn N − n f f + Nn f − f ( (2 ) (2 ) ) , 1 2 R = − Δ + ν −ν n + ν −ν N Q n = 2gQ, N = −gQ, f = gQ 1  , f = −gQ 2  , where 1 2 Δ = 2ω −Ω+ω −ω – resonance detuning. The main equation, describing the time evolution of molecule densities N, it is convenient to present as equation of evolution of nonlinear oscillator (dN / dt )2 +W(N) = 0 , where = − Λ −Λ + + Λ + 2 + 2 1 0 1 2 0 W(N) (N N ) (( / 2 )(N N ) δ ) 16 (1/ 2 ) ( )( ). 0 10 0 20 N − N 2 N − N + f N − N − f Here δ = Δ / g, (2 ) / , 1 1 Λ = ν −ν g (2 ) / 2g 2 2 Λ = ν −ν is the normalized resonance detuning and coefficients interparticle interaction. There is a special regime of interparticle interaction, in which we observe the effect of self-trapping for the case when the constants of interatomic, intermolecular and atomic–molecular interaction are not equal to zero. We study further the dynamic of atom–molecular conversion subject to process of into particle interaction when resonance detuning equals zero. In this case may happen the effect of self-trapping in the system. When constants of interatomic, intermolecular and atomic–molecular interaction does not equal zero we can observed the self-trapping. When constants of interaction equals zero this effect cannot be observed. It is natural that the potential energy includes parameters which determines the presence of self-trapping.