The zero point energy of the crystals of LiH and LiD is approximated in two different ways. In the first place a formula of London, found by quantisation of the mean free path in condensed systems of rigid spheres, is applied. Adjusting a parameter so as to find the right difference of lattice constants between LiH and LiD yields reasonable values of the zero point energy. In the second place, in a purely theoretical investigation of the lattice vibrations by means of the general theory of Lyddane and Herzfeld for polar crystals of the sodium chloride type, the zero point energies of ( E0) LiH = 5,49 kilocalories/mol and ( E0) LiD = 4,30 kilocalories/mol are calculated. The origins of these high values and the limitations of the theory are discussed.