Quasielastic neutron scattering was used to investigate the low energy transfer dynamics of the complex borohydrides Mg(BH₄)₂ in the α- and β-modifications, LiBH₄ in the low and high temperature crystal structure, and an 1 : 1 molar mixture of LiBH₄ + α-Mg(BH₄)₂. All investigated compounds show a rich dynamic behaviour below an energy range of ΔE = 10 meV with the superposition of rotational dynamics of the constituent [BH₄]¯ anions and low lying lattice modes. For Mg(BH₄)₂, the rotational diffusion of the [BH₄] units was found to be much more activated in the metastable β-polymorph compared to the α-phase, and the low lying lattice modes are even softer in the former crystal structure. In Mg(BH₄)₂, the structural phase transition is mainly governed by the lattice dynamics, while alkaline LiBH₄ exhibits a transition of the [BH₄] rotations around the phase transition temperature. Ball milled LiBH₄ + α-Mg(BH₄)₂ remains a physical mixture of the parent compounds and each component retains its characteristic dynamic signature up to the melting temperature.