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The third-order optical nonlinearities and responses of a squarylium dye, 2,4-di-3-guaiazulenyl-1,3-dihydroxycyclobutenediylium dihydroxide, in tetrahydrofuran (THF) solution and in polystyrene (PS) coating films are measured by the femtosecond degenerate four-wave mixing technique under resonant conditions. The molecular hyperpolarizability γ of the squarylium dye in the THIF solution is determined to be 3.0 × 10-29 esu at 764nm, and its electronic component γe is determined to 5e 1.1 × 10-29 esu. The third-order nonlinear susceptibility χ(3) of one of the present PS coating films containing the squarylium dye is as high as 3.1 × 10-8 esu at 800nm, and its electronic component χe(3)is 1.3 × 10-8 esu.