  We present a theory of the quantum Griffiths phases associated with the
ferromagnetic quantum phase transition in disordered metals. For Ising spin
symmetry, we study the dynamics of a single rare region within the variational
instanton approach. For Heisenberg symmetry, the dynamics of the rare region is
studied using a renormalization group approach. In both cases, the rare region
dynamics is even slower than in the usual quantum Griffiths case because the
order parameter conservation of an itinerant ferromagnet hampers the relaxation
of large magnetic clusters. The resulting quantum Griffiths singularities in
ferromagnetic metals are stronger than power laws. For example, the low-energy
density of states $\rho(\epsilon)$ takes the asymptotic form
$\exp[\{-\tilde{\lambda}\log (\epsilon_0/\epsilon)\}^{3/5}]/\epsilon$ with
$\tilde{\lambda}$ being non-universal. We contrast these results with the
antiferromagnetic case in which the systems show power-law quantum Griffiths
singularities in the vicinity of the quantum critical point. We also compare
our result with existing experimental data of ferromagnetic alloy
${\rm{Ni}}_{x}{\rm{V}}_{1-x}$.
