The nonlinear response of three degree of freedom vibratory system with double pendulum in the neighborhood internal and external responses have been researched. Numerical and analytical methods have been applied for these investigations. Analytical solutions have been obtained by using multiple scale method. This method is used to construct first-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters. Numerically it was shown, that near internal and external resonances except different kinds of periodic vibrations there may also appear chaotic vibration. For characterizing an irregular chaotic response bifurcation diagrams and time histories, Poincare` maps and maximal exponents of Lyapunov have been constructed.

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