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 ƒ(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 ƒ(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 ƒ(hc) in a given sample is determined primarily by the grain size d and the dislocation density ρ. A nearly constant ƒ(hc) occurs in grains with small d and/or ρ, but a Gaussian f(hc) is approached with increasing d and/or ρ. The transition from L‐type to H‐type behavior in the Lowrie‐Fuller test occurs at a critical grain size dt ≈ 2/(ρw), 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.