We have developed a new specialized version of the fast multipole method (FMM) for dipolar systems. For this purpose we have derived general expressions of the multipole expansion coefficients (in spherical coordinates) for a system of point dipoles with the potential phi(dip)similar to 1/r(2). Our version is especially useful for simulations of fine magnetic particle systems (magnetic nanocomposites, ferrofluids), molecular dipolar fluids or electric dipolar glasses. (C) 2003 Elsevier B.V. All rights reserved.