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The dynamical instability of relativistic polytropic spheres, embedded in a spacetime with a repulsive cosmological constant, is studied in the framework of general relativity. We apply the methods used in our preceding paper to study the trapping polytropic spheres with Lambda = 0, namely, the critical point method and the infinitesimal and adiabatic radial perturbations method developed by Chandrasekhar. We compute numerically the critical adiabatic index, as a function of the parameter sigma = p_c/(rho_c)^2, for several values of the cosmological parameter lambda giving the ratio of the vacuum energy density to the central energy density of the polytrope. We also determine the critical values for the parameter sigma_cr, for the onset of instability, by using both approaches. We found that for large values of the parameter lambda, the differences between the values of sigma_cr calculated by the critical point method differ from those obtained via the radial perturbations method. Our results, given by both applied methods, indicate that large values of the cosmological parameter lambda have relevant effects on the dynamical stability of the polytropic configurations.