We develop a theory of acquisition and alternating field (AF) demagnetization of anhysteretic remanence (ARM) and saturation isothermal remanence (SIRM) in multidomain (MD) grains in order to better understand the Lowrie-Fuller test. Our theory shows that the relative stabilities of low-field ARM and high-field SIRM against AF demagnetization are determined by the distribution f(hc) of microcoercivity hc in a sample, as found earlier by Bailey and Dunlop. When f(hc) is nearly constant, weak-field ARM is more resistant to AF demagnetization than SIRM. In contrast, when f(hc) varies exponentially or is a Gaussian distribution, SIRM is more AF resistant than ARM. These contrasting stability trends are conventionally called single-domain (SD)-type and MD-type Lowrie-Fuller results, respectively, but in reality, both types occur in the MD size range. We propose instead the descriptive terms L-type result (low-field remanence, i.e., ARM, more stable) and H-type result (high-field remanence, i.e., SIRM, more stable). The Lowrie-Fuller test does not distinguish one type of domain structure from another, but it does depend indirectly on grain size. We show that the distribution f(hc) in a given sample is determined primarily by the grain size d and the dislocation density &rgr;. A nearly constant f(hc) occurs in grains with small d and/or &rgr;, but a Gaussian f(hc) is approached with increasing d and/or &rgr;. The transition from L-type to H-type behavior in the Lowrie-Fuller test occurs at a critical grain size dt≈2/(&rgr;w), where w is the domain-wall width. The lower the dislocation density, the larger the transition size in the Lowrie-Fuller test. This simple relationship explains the increase in the transition size from about 5--10 μm observed for crushed magnetite grains to ≈100 μm for hydrothermally grown magnetites, which have lower dislocation densities than crushed grains. ¿ American Geophysical Union 1995