An experimental study was carried out to investigate the thermal demagnetization properties of partial thermoremanent magnetization (pTRM). Fifteen different igneous rocks and five synthetic specimens containing crushed and hydrothermally grown magnetite of different grain sizes were studied. The domain structures (DS) of the samples cover the range from single domain (SD) to multidomain (MD) grains. Two different kinds of pTRM were considered: (1) pTRMa(T1,T2) acquired when the upper temperature T1 of acquisition of pTRM is reached by cooling from Tc and (2) pTRMb(T1,T2) acquired by heating to T1 from room temperature. As was shown previously, Thellier's laws of independence and additivity of pTRM(T1,T2) are violated in MD grains. The violations are as follows (1): There is a decrease of pTRM(T1,T2) on cooling below the lower temperature T2 of acquisition of pTRM; (2) the intensity of pTRM(T1,T2) depends on the thermal prehistory of the sample, e.g., pTRMb(T1,T2)≠pTRMa(T1,T2); and (3) a pTRM(T1,T2) has a rest (tail) that is not removed by thermal demagnetization at T1c. Here is shown that the violations of the Thellier's laws occur simultaneously and are most pronounced in MD grains. Deviations from both laws are much weaker or almost absent for SD and pseudosingle-domain (PSD) particles. The properties of pTRM(T1,T2) depend strongly on the temperature interval (T1,T2) where the pTRM was induced. Half of the natural samples under consideration have MD or PSD properties for the low-temperature pTRMs combined with typical SD-PSD behavior for the high-temperature pTRMs. A linear relation was found for MD samples which states that pTRMa(T1,T2)-pTRMb(T1,T2) is equal to intensityof a tail of pTRMa(T1,T2) after thermal demagnetization at T1. This relationship implies that the remanence carriers, which constitute the tail of pTRMa, do not participate in the acquisition of pTRMb. A modification of N¿el's <1955> thermofluctuation model of MD TRM is proposed to explain this relation. The modification suggests that variations of DS during a cooling and heating cycle result in their stabilization accompanied by an irreversible increase of unblocking temperatures. The normalized value of the tail of pTRMa(300 ¿C,Tr) after demagnetization is suggested as an independent means to evaluate the DS of a sample. ¿ 2000 American Geophysical Union