Measurements of geomagnetic paleointensity using the Thelliers' double-heating method in vacuum have been made on 10 specimens of submarine pillow basalt obtained from 7 fragments dredged from localities 700,000 years old or younger. In the magnetic minerals, the titanium/iron ratio parameter x and the cation deficiency (oxidation) parameter z were determined by X-ray diffraction and Curie temperature measurement. Fresh material (z?0) provided excellent results: most of the natural remanent magnetization (NRM) could be thermally demagnetized before the magnetic minerals became altered, and the NRM-TRM lines were straight and well constrained, and geologically reasonable paleointensities were obtained. Somewhat oxidized material (z?0.2) also provided apparently valid paleointensities: values were similar to those from fresh specimens cut from the same fragments, although only half or less of the NRM could be thermally demagnetized before alteration of the magnetic minerals. More highly oxidized material (z?0.6) gave a result seriously in error: the paleointensity value is much too low, because of continuous diproportionation of titanomaghemite during the heating experiments and because seafloor weathering had decreased the NRM intensity. From limited published data, the extent of oxidation of titanomagnetite to cation deficient titanomaghemite in pillow basalt exposed on the seafloor appears to be approximately z=0.3 at 0.2--0.5 m.y., z=0.6 at 1 m.y., and z=0.8--1.0 at 10--100 m.y. This implies that valid paleointensities can be obtained from exposed submarine basalt, but only if the basalt is younger than a few hundred thousand years. Equally good paleointensities were obtained from strongly magnetized (H-type) basalt and moderately magnetized (L-type) basalt. The degree of low-temperature oxidation of cubic iron-titanium oxides in submarine basalts correlates very well with the diminution of amplitude of linear magnetic anomalies when both are compared as a function of crustal age. Systematic radial variation of Curie temperature is a primary feature of submarine basalt pillows, so that estimation of the oxidation parameter z from the Curie temperature alone by assuming a value for x can be in error. Reasonably precise and self-consistent values of both x and z can be obtained if both the cubic cell dimension and the Curie temperature of the cubic oxide are measured.