The melting transition of free clusters of sulfur hexafluoride containing 229 and 965 molecules has been studied by molecular dynamics (MD) simulation using a massively parallel transputer-based computing surface. A comparison between the performance of our computer and that of a Cray XMP for the same calculation is made in the text. The stable high temperature structure for SF6 clusters of a few hundreds of molecules is the BCC lattice. as in the natural crystal. Moreover, we show that the core of such clusters behaves from both the static (densities) and dynamic (orientational disorder, self diffusion) points of view like an infinite crystal. As a result of this, the melting process is found to be very similar to that of a true crystal: melting initiates at the surface and then propagates into the bulk. However, the surface-to-volume ratio is much larger than expected in a natural crystallite, and this leads to a lowering of the melting temperature, as predicted by the Gibbs-Thompson relation. Surface melting in our cluster is initiated by surface vacancy formation. This leads first to a highly disordered surface having self-diffusion coefficients of the order of the bulk liquid, but remaining clearly crystalline. In the last approximately 10 K below melting, a continuous change from a solid-like to a fluid-like surface occurs while the surface disordering propagates into the centre of the cluster.