We analyze the potential of the e+e- Linear Colliders, operating in the e-gamma and gamma-gamma modes, to probe anomalous quartic vector--boson interactions through the multiple production of Ws and Zs. We examine all $SU(2)_L otimes U(1)_Y$ chiral operators of order p^4 that lead to new four--gauge--boson interactions but do not alter trilinear vertices. We show that the e-gamma and gamma-gamma modes are able not only to establish the existence of a strongly interacting symmetry breaking sector but also to probe for anomalous quartic couplings of the order of 10^{-2} at 90% CL. Moreover, the information gathered in the e-gamma mode can be used to reduced the ambiguities of the e+e- mode.
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