  The spin dynamics in [TbPc$_{2}$]$^{0}$ and [DyPc$_{2}$]$^{0}$ single
molecule magnets have been investigated by means of muon and nuclear
spin-lattice relaxation rate measurements. The correlation time for the spin
fluctuations was found to be close to 0.1 ms already at 50 K, about two orders
of magnitude larger than the one previously found in other lanthanide based
single molecule magnets. In [TbPc$_{2}$]$^{0}$ two different regimes for the
spin fluctuations have been evidenced: a high temperature activated one
involving spin fluctuations across a barrier $\Delta\simeq 880 K$ separating
the ground and first excited states and a low temperature regime involving
quantum fluctuations within the twofold degenerate ground-state. In
[DyPc$_{2}$]$^{0}$ a high temperature activated spin dynamics is also evidenced
which, however, cannot be explained in terms of a single spin-phonon coupling
constant.
