Expressions for the dipolar and hyperfine contributions to the relaxation rate of muons implanted in a ferromagnet are presented, and analysed using the Heisenberg model of spin waves including dipolar and Zeeman energies. Calculations for EuO indicate that the temperature dependence of the hyperfine and dipolar contributions to the relaxation rate are similar, so the latter contribution will dominate if the ratio of the hyperfine and dipolar coupling constants is indeed very small. The hyperfine mechanism is sensitive to the dipolar energy of the atomic spins, whereas the dipolar mechanism depends essentially on the exchange energy. For both mechanisms there is an almost quadratic dependence on temperature, throughout much of the ordered magnetic phase, which reflects two-spin-wave difference events from the Raman-type relaxation processes.