The thermoremanent magnetization (TRM) of ten igneous rocks with grain sizes varying from fine to coarse varies with applied field H as H p in fields 0.5Oe< H < 8–22Oe and as H p for 8–22Oe< H < 90–140Oe. Domain structure was investigated using alternating-field demagnetization (the Lowrie-Fuller test), the Koenigsberger ratio Q t , and saturation hysteresis parameters. Five of the rocks (three basalts and two diabases) appear to contain mostly single-domain (SD) or pseudo-single-domain (PSD) grains, two contain a mixture of coarse multidomain (MD) and ultra fine SD grains (the latter as impurities in silicates), and three contain largely MD grains above PSD size. However, there was no correlation of p and q values with either domain structure or degree of alteration upon heating. In spite of the wide range of grain sizes and domain structures, the high-field results were all consistent with a generalized version of Néel's two-domain model for TRM. The generalization presented here agrees with the predictions of independent approaches by Everitt and Schmidt. According to the theory, p = 1 and q = 1 − (1/n), where n is the index in the experimental power law variation of coercive force H c with saturation magnetization J s at high temperature, H c(T) ∝ J s n (T) . In practice, the former prediction is generally masked by the presence of PSD moments at low fields. The latter prediction was tested by determining n from high-temperature hysteresis measurements. Agreement between q determined from TRM data and 1 − (1/n) was poor for samples that altered upon heating. The agreement was somewhat better but not convincing for relatively unaltered samples. TRM and coercive force data for four PSD magnetite powders and two SD cobalt ferrite powders were also analysed. A definite grain-size trend was found with the magnetites: q increased with increasing grain size (0.04 μm to 0.22 μm) from 0.28 to 0.43 while 1 − (1/n) increased from 0.32 to 0.49. However, the fact that the TRM data for the SD cobalt ferrites also could be fit by the generalized theory casts doubt on the validity of the entire model, which is based on the motion of a domain wall in the presence of an internal demagnetizing field. Although the physical processes involved remain unclear, the data clearly indicate a previously unsuspected similarity in the TRM behaviour of SD, PSD and MD magnetite, spanning a size range 0.04 to > 100 μm.