Based on density-functional theory and density-functional perturbation theory we have studied the thermodynamical and vibrational properties of Mg(AlH4)(2). The crystal structure recently proposed on the basis of x-ray powder-diffraction data has been confirmed theoretically by the comparison of the experimental and theoretical IR and Raman spectra. The main discrepancy regards the position of the hydrogen atoms which makes the theoretical AlH4 tetrahedra more symmetric than that experimental inferred from data. The calculated thermodynamical decomposition temperature is also in good agreement with the experimental result.