In this work we present a first-principles density functional study of the electronic, vibrational, and structural properties of ZnGa2O4 and ZnAl2O4 spinel structures. Here we focus our study in the evolution of the structural properties under hydrostatic pressure. Our results show that ZnGa2O4 under pressure has a first-order phase transition to the marokite (CaMn2O4) structure, which is in good agreement with recent angle-dispersive x-ray diffraction experiments. We also report a similar study for the ZnAl2O4 spinel; we found that this compound under pressure has a first-order phase transition to the orthorhombic CaFe2O4-type structure. Our results in both compounds support, under nonhydrostatic condition, the possibility of a second-order phase transition from the cubic spinel to the tetragonal spinel as reported experimentally in ZnGa2O4.