The lowering of the Curie temperature of a ferromagnetic substance by random dilution with non-magnetic elements is studied on the basis of Heisenberg and Ising models having nearest-neighbour interactions between magnetic elements only. It is proved that the limiting concentration,pc, of magnetic elements, below which there is no Curie temperature, is the same for all such models, whether Heisenberg or Ising and regardless of the spin value concerned: it depends only on the lattice structure. Numerical estimates ofpcare given for various lattices. Successive approximations are developed to the full Curie temperature curve, and it is found that whereas for the Ising modelTc(p) approximates topTc(1) nearp=1,Tc(p)<pTc(1) for the Heisenberg model.