With a view to determine the effect on the material properties of the interplay between oxygen ordering and the diffusive motion of metal-ion dopants in YBa 2 Cu 3 - y M y O 6 + x (M = Co, Fe, Al) we have developed, for a specific statistical mechanical model, a Monte Carlo computer-simulation algorithm in optimized C * and implemented the program on a 8192-processor CM200 Connection Machine. The algorithm, which allows for the simultaneous diffusive motion of oxygen atoms and metal ions, takes full advantage of all single-bit processors available on a CM200. Performance on the CM200 is compared with that on a 65536-processor CM2 as well as various serial workstations. The simulation results on the physical model show in the case of small oxygen concentrations significant metal-ion domain-formation effects related to phase separation into a phase with dense packing of oxygen and metal-ion dopants. At high oxygen concentration, a dispersed phase is found with a strong tendency towards formation of extended O-M-O-M chains. The results are briefly discussed in relation to experiments on YBa 2 Cu 3 - y Fe y O 6 + x .