It is suggested that in many ferromagnetic materials there may occur particles distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector. As the field changes continuously, the resolved magnetization may change discontinuously at critical values of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle and on the orientation of easy axes with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magnetocrystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution, along with a less detailed treatment for the general ellipsoidal form.