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The finite temperature dynamics of the Dyson hierarchical classical spinsmodels is studied via real-space renormalization rules concerning the couplingsand the relaxation times. For the ferromagnetic model involving Long-Rangedcoupling $J(r) \propto r^{-1-\sigma}$ in the region $1/2<\sigma<1$ where thereexists a non-mean-field-like thermal Ferromagnetic-Paramagnetic transition, theRG flows are explicitly solved: the characteristic relaxation time $\tau(L)$follows the critical power-law $\tau(L)\propto L^{z_c(\sigma)} $ at the phasetransition and the activated law $\ln \tau(L)\propto L^{\psi} $ with$\psi=1-\sigma$ in the ferromagnetic phase. For the Spin-Glass model involvingrandom Long-Ranged couplings of variance $\overline{J^2(r)} \proptor^{-2\sigma}$ in the region $2/3<\sigma<1$ where there exists anon-mean-field-like thermal SpinGlass-Paramagnetic transition, the coupled RGflows of the couplings and of the relaxation times are studied numerically :the relaxation time $\tau(L)$ follows some power-law $\tau(L)\proptoL^{z_c(\sigma)} $ at criticality and the activated law $\ln \tau(L)\proptoL^{\psi} $ in the Spin-Glass phase with the dynamical exponent$\psi=1-\sigma=\theta$ coinciding with the droplet exponent governing the flowof the couplings $J(L) \propto L^{\theta} $.

Real-space renormalization for the finite temperature statics and dynamics of the Dyson Long-Ranged Ferromagnetic and Spin-Glass models