The magnetic, magnetorheological, and magnetostrictive behavior of nonlinear magnetizable particles in a nonmagnetic continuum is considered. The magnetization of isolated spheres in a uniform magnetic field is solved exactly for the case where the field-dependent, sphere permeability is given by the Frohlich-Kennelly equation. This solution is incorporated into a point-dipole model for suspensions composed of aligned, isolated chains of spheres. The suspension magnetization and shear storage modulus reflect the nonlinear magnetization, saturating at large field strengths, consistent with some experimental observations and in agreement with previous calculations. Analysis of the magnetostrictive behavior reveals that additional magnetostriction parameters are required compared to materials whose magnetization is linear in the applied field. (C) 2001 The Society of Rheology.