In this work we present a first-principles density functional study of the vibrational properties of ZnAl₂O₄ and ZnGa ₂O₄ as function of hydrostatic pressure. Based on our previous structural characterization of these two compounds under pressure, herewith, we report the pressure dependence on both systems of the vibrational modes for the cubic spinel structure, for the CaFe₂O₄-type structure (Pnma) in ZnAl₂O₄ and for marokite (Pbcm) ZnGa₂O₄. Additionally we report a second order phase transition in ZnGa₂O₄ from the marokite towards the CaTi₂O₄-type structure (Cmcm), for which we also calculate the pressure dependence of the vibrational modes at the Γ point. Our calculations are complemented with Raman scattering measurements up to 12 GPa that show a good overall agreement between our calculated and measured mode frequencies.