The partial and the integral enthalpies of mixing of liquid Al-Cu-Ni-Si alloys have been determined by high temperature isoperibolic calorimetry for four isopleths at 1575+/-3 K. A least-square regression analysis of the data together with the literature values of the constituent binaries and ternaries results a consistent analytical representation of the enthalpy of mixing of liquid Al-Cu-Ni-Si alloys at 1575 K. The regular association model describes adequately the thermodynamic properties of the liquid constituent ternaries on the basis of their constituent binaries, respectively, if additional ternary association reactions with the stoichiometries Al2Cu1Ni1, Al1Cu3Si1, Al1Ni2Si1, and Cu2Ni2Si1 are assumed. The calculated Gibbs energy for the ternaries demonstrate that there are minima for the Al-Cu-Ni (-42.8 kJ mol(-1)), Al-Ni-Si (-54.6 kJ mol(-1)), Al-Cu-Si (-24.4 kJ mol(-1)) near the ternary compositions Al0.45Cu0.10Ni0.45, Al0.20Ni0.55Si0.25, and Al0.17Cu0.50Si0.33, respectively, whereas the minimum for the liquid Cu-Ni-Si alloys (-52.0 kJ mol(-1)) corresponds to the binary composition Ni0.58Si0.42. The Gibbs energy of liquid quaternary alloys were estimated on the basis of the results from the regular association model for the constituent ternaries using the Kohler scheme in combination with an empirical enthalpy-entropy model. The minimum of the Gibbs energy of mixing of the quaternary alloys is observed at the composition Al0.19Cu0.08Ni0.50Si0.23.