A separation of variables method based on expansions of the electromagnetic fields in terms of spherical wave functions is expanded at nonspherical (axisymmetric) particles with a rather large number of layers. Commonly used alternative approaches to systems of linear algebraic equations relative to unknown field expansion coefficients for layered particles are considered in some detail. The SVM code developed is compared with the EBCM, GMT and DDA codes designed for multilayered scatterers and some numerical results obtained for nonspherical scatterers with up to 100 layers are presented as illustrations.