Electric birefringence has been measured at a wavelength of 632.8 nm over a range of temperature and pressure in the gases CH4, CH3F, CH2F2, CHF3 and CF4. The results yield values of the second hyperpolarizability γ for CH4 and CF4 and, for CH3F, CH2F2 and CHF3, the first hyperpolarizability β and the difference (α33-α) between the optical polarizability component in the direction of the molecular dipole and its mean. For CH2F 2 (α33-α) is unusually small; the birefringence changes sign as the pressure is increased, the change occurring at 1.7 bar at 244°K. Limitations of a bond additivity model for β are exposed, and the importance of hyperpolarizability contributions to the Kerr constant demonstrated. The density dependence of the birefringence in the five gases is compared with the predictions of simple theoretical models, but agreement is in most cases poor.