Dedicated to Ulrich Eckern on the occasion of his 60th birthday.The Heisenberg exchange parameters for the Heusler compound Co 2 NiGa with L2 1 structure were calculated using the Korringa-Kohn-Rostoker method and by employing the magnetic-force theorem to obtain the total energy changes associated with the local rotation of magnetization direction. The crystal structure was subjected to pressure and the corresponding dependence of the magnetic exchange couplings were determined. Curie temperatures obtained by applying mean field theory (MFT) reveals a slightly nonlinear decrease with pressure and it is related to the changes of the magnetic moment and the electronic density of states. Further investigation of the pressure dependence of the Curie temperature and magnetization suggests that this particular compound is a weak itinerant ferromagnet. Analysis of the magnetic properties of the Co 2 NiGa compound using Monte Carlo simulations reveals a significant effect of pressure on the magnetization and magnetic susceptibility of the structure. The spin dynamics was modeled by applying the Landau-Lifshitz-Ginzburg equation to a Heisenberg Hamiltonian. The magnon spectra along the [100] direction is obtained through the Fourier transform of the dynamic correlation function for the predefined set of exchange parameters and pressure. We find a large dependence of the magnon dispersion relation with pressure and in particular of the magnetic excitations gap.