[en] We develop a precise power counting rule (a generalization of Weinberg's counting method for the nonlinear sigma model) for the electroweak theories formulated by chiral Lagrangians. Then we estimate the contributions of all next-to-leading order (NLO) bosonic operators to the amplitudes of the relevant scattering processes which can be measured at high energy colliders, such as the LHC and future Linear Colliders. Based upon these results, we globally classify the sensitivities of testing all NLO bosonic operators for probing the electroweak symmetry breaking mechanism at high energy colliders. (orig.)