The authors consider nonlinear equation systems of the form \[ g_i(x) = 0, i = 1, \dots, N, \] where \(g_i:\mathbb R^n \to\mathbb R\) are continuously differentiable functions. The traditional approach to such problems, which minimizes the sum of the squared residuals may fail in the presence of singularities of the Jacobian matrix or if the initial solution guess is far away from the solution of the given problem. To overcome these difficulties, the authors propose to formulate a generic programming problem by a proper set of ordinary differential equations, whose equilibrium points correspond to the solutions of the given problem. The proposed method is described, its asymptotic stability is demonstrated. Effectiveness of the proposed approach is shown on numerical results presented in the concluding part of the paper.