Experimental observation of the phenomenon of the Bose–Einstein condensation (BEC) in dilute, trapped alkali–metal vapors has opened a new context for studying of the properties of mesoscopic systems in the field of low–temperature physics. In recent years, investigation into the dynamics of bound atomic–molecular condensates under the conditions, when the Feshbach resonance are manifested or under the conditions of the atomic–molecular Raman conversion involving two electromagnetic pulses have been attracting special attention. At present, the production of ultracold Bose–condensed two-, three- and four-anomic homo- and heteronuclear molecules has been observed. Below we propose a general type of nonlinearity, which can arise through atomic–molecular coupling, i.e. it may lead to the formation of a molecular Bose–condensate via the emission of molecular bosons from the atomic Bose–condensate, which is stimulated by two Raman pulses. We investigated the dynamics of the atomic–molecular BEC treating the Raman process of binding of two different Bose–condensed atoms into heteronuclear molecule as an indivisible process. We suppose that two different free Bose–condensed atoms with zero kinetic energy pass to a lower molecular state via an excited molecular state by absorbing and emitting light quanta with different frequencies. In this case two phasecoherent pulses with certain values of field amplitudes and phases are used. Binding of each pair of atoms into a molecule leads to a transfer of a photon from the first pulse to the second one. For this reason enhancement of one pulse and suppression of the other during atomic–molecular conversion could serve as an indication of a coherent process. In the frame of mean–field approximation we have obtained the nonlinear differential equation, which describes the dynamics of the density of molecules. The process rate depends very strongly on the initial densities of molecules and atoms, on the initial phase difference and on the resonance detuning. We have obtained exact solutions of equations in the terms of hyperelliptical integral. We considered a number of results using the different approximations, for example, the approximations of given densities of the photons, of the atoms and other, for which we obtained the exact solutions in terms of elliptical Jacoby functions and the expressions for the periods of oscillations. It is shown that conversion may be periodic in time. The amplitude and period of oscillations of the density of molecules depend on the initial densities of particles and initial phase difference. The special solution – the rest – of the system for nonzero initial densities of particles is predicted. It is pointed out that coherence of the Bose condensate of atoms, molecules and photons predetermines the possibility of phase control of the conversion process and the onset of the ultracold coherent superchemical reactions.