We present an experimental study of the nonlinear optical absorption of the eutectic mixture E7 at the nematic-isotropic phase transition by the Z-scan technique, under continuos-wave excitation at 532 nm. In the nematic region, the effective nonlinear optical coefficient β, which vanishes in the isotropic phase, is negative for an extraordinary beam and positive for an ordinary beam. The parameter S NL , whose definition in terms of the nonlinear absorption coefficient follows the definition of the optical-order parameter in terms of the linear dichroic ratio, behaves like an order parameter with critical exponent 0.22 ± 0.05, in good agreement with the tricritical hypothesis for the N-I transition.