Author: Y.A.Ryabov Title:"Analytic-numerical solutions of three bodies problem with the aid of a computer". There ar considered iterations algorithm for construction of quasi-periodic solutions of differential systems with slow positional and fast angular variables analogous to system for a restricted three bodies problem.Features of this algorithm are following: a)quadratic convergence if there are no sharp resonances between initial angular velocities;b)involves procedures only of classical type for calculations of successive approximations;c)realisation of algorithm on each step involves operations on Fourier polinomials (multiplications, substitutions of one polinomials into other, etc.) and solutions of linear algebraic systems of high order.