Studies of processes in coupled nonlinear oscillators have many important applications.In particular,it is known that in a system of incoherently excited oscillators a part of the energy can be spontaneously transformed to coherent radiation.Actually,a similar phenomenon defines the work of quantum systems such as lasers and the atoms emitting the so-called superradiance [1].Recently the quantum amplification and generation of sound(a “SASER” problem)have been studied [2].Classical analogs of such systems have also been considered in relation to various applications such as the powerful millimeter-and submillimeter range electronic generators [3],gas bubbles in acoustics [4],ecological and biological systems(e.g.,[5,6]).Besides,such systems have a significant general interest in nonlinear dynamics as examples of the “chaos-order” transition [7].Mathematically,different approaches were used for description of processes in systems of coupled oscillators.In [5,6] the oscillators were supposed to be continuously distributed over their resonance frequencies,whereas their amplitudes do not vary.In [8] a direct numerical calculation for a system of 100 oscillators was performed.In [9,10] a system of nonlinear oscillators with varied phases and amplitudes are considered analytically using groups of oscillators with different phasing.In all the aforementioned cases of the main interest is the coherent part of the field(the order parameter),which defines the total energy of the collective coherent process.Although a general possibility of self-synchronization of the ensembles of nonlinear oscillators is well established,a number of important questions remain unresolved.Among them is a problem of efficiency: what part of the total energy of the initial incoherent oscillations is transformed to the coherent radiation,and how does the efficiency depends on the number of oscillators and the nonlinearity.Another problem is comparison of the approximate analytical models(which are relatively simple)with the direct computation of the differential equations for a large population of interacting oscillators.The goal of this presentation is twofold.First,it provides a brief review of the main results in the area.Second,it describes new results of study of a system of coupled,Duffing-type oscillators,for different discrete numbers of them(100,200,and 256,in particular),a broad range of amplitude and nonlinearity parameters,and random initial conditions.We compare the results of direct numerical solutions for the time evolution of the coherent field with the simplified analytical,modal description mentioned above.Numerical simulations of nonlinearly coupled oscillators favorably agree with the theoretical model for a relatively small nonlinearity.Whereas the most detailed results refer to the dissipative coupling(such as via the joint energy radiation),the case of reactive coupling when the system remains Hamiltonian,is also considered.Some new problems which deserve to be studied are outlined in conclusion.