Monte Carlo type computer simulations of random substitutional alloys containing magnetic solutes in nonmagnetic metal matrices have been used to determine critical concentrations for ferromagnetism and the average number of interactions per magnetic atom in ferromagnetic alloys. Calculations were carried out for both FCC and BCC lattices using two different interaction models: Model A assumed ferromagnetic interactions between first near neighbor magnetic atoms only (1NN); Model B assumed ferromagnetic interactions between both first and second near neighbor magnetic atoms (1NN+2NN). Comparisons of model B for a FCC lattice with the experimental data for quenched Au ¯ Fe alloys show excellent agreement for both the onset of ferromagnetic order, and for the concentration dependence of the superparamagnetic behavior in lower concentration nonferromagnetic alloys. For higher concentration alloys a direct relationship has been found between the experimental Curie temperatures and the average number of ferromagnetic interactions per magnetic atom in the model.