The effect of anomalous couplings in γγ → W + W − is studied for different energies of the γγ mode of the next linear collider. The analysis based on the maximum likelihood method exploits the variables in the four-fermion semi-leptonic final state. Polarised differential cross sections based on the complete set of diagrams for these channels with the inclusion of anomalous couplings are used and compared to an approximation based on γγ → W + W − with full spin correlations. To critically compare these results with those obtained in e + e − we perform an analysis based on the complete calculation of the four-fermion semi-leptonic final state. The anomalous couplings that we consider are derived from the next-to-leading order operators in the non-linear realisation of symmetry breaking. quite difficult to disentangle a W W γ and a W W Z coupling at the e + e − mode, whereas obviously only the former can be probed at the γγ mode. However, as we will argue, the electroweak precision measurements at the Z peak are a sign that there should be a hierarchy of couplings whereby the symmetries one has observed at the present energies indicate that the W W γ and the W W Z should be related. If this is so, though γγ → W + W − is unique in unambiguously measuring the W W γ couplings, it is somehow probing the same parameter space as e + e − → W + W − . In such an eventuality one should then enquire about how to exploit the γγ mode, and whether the reaction γγ → W + W − can give more stringent constraints than in the e + e − mode. In addition it is useful to investigate whether one may gain by combining the results of the γγ analysis with those obtained in 1 the e + e − mode. These two aspects will be addressed in the present paper.Although there have been numerous studies that dealt with the subject of the tri-linear anomalous couplings in γγ → W + W − [11], they have all been conducted at the level of the γγ → W + W − cross section. As we will show, even if one assumes reconstruction of the helicities of the W , restricting the analysis of the γγ → W + W − at the level of the cross section, where one only accesses the diagonal elements of the W W density matrix, it is not possible to maximally enhance the effect of the anomalous couplings. Indeed, as one expects in an investigation of the Goldtsone sector, the new physics parameterised in this context by an anomalous magnetic moment of the W , ∆κ γ , affects principally the production of two longitudinal W bosons. In the γγ mode this affects predominantly the J Z = 0 amplitude by providing an enhanced coupling of the order γ = s γγ /M 2 W ( √ s γγ is the γγ centre of mass energy). Unfortunately the same standard amplitude (the J Z = 0 with two longitudinal W's) has the factor 1/γ and therefore the interference is not effective in the sense that the genuine enhanced coupling γ brought about by the new physics is washed out. This is in contrast with what happens in the e + e − mode where the interference is fully effective. Nonetheless, the enhanced coupling could still be ex...