This study gives our calculation for the specific heat close to the phase transitions from the disordered (phase 11) to the antiferro-ordered (phase 111) and to the ferro-ordered (phase IV) phases in ND4Br. We calculate the specific heat C-VI due to the nearest-neighbour interactions between ND4+. tetrahedra in the ND4Br crystal, by using an Ising model superimposed on an Einstein and/or Debye model which we have developed. Our calculated specific heat C-VI agrees well with the experimental C-p data for the phases 11, 111 and IV in ND4Br. This shows that our model is adequate to describe the observed behaviour of the ND4Br crystalline system close to its upper (T-c = 214.86 K) and lower (T-c = 166.7 K) transitions. (C) 2002 Elsevier Science B.V. All rights reserved.