A spin-Hamiltonian that describes the orientational energy of nanoscopic magnetic particles is presented. A few short observations on spin tunneling are made. Basic ideas on superparamagnetism and classical results of calculations of relaxation times are presented. A model for spin–phonon interaction induced spin reversals is proposed and the relaxation time for spin jumps between next nearest spin levels (ΔS z =¡À2) is calculated. M?ssbauer patterns are simulated by means of a multi-level method for spin transitions between next nearest and nearest (ΔS z =¡À1) spin levels. The simulations with (ΔS z =¡À1) show better concordance with experimental spectra and allow the use of a reduced spin, which speeds up considerably the calculations and allows to include particle size distribution.