Grain coarsening of alloys in the semi-solid state is important in controlling grain sizes in spray forming and in other processes in which an alloy is formed or cast in the semi-solid state. Until now, this coarsening has been analysed in terms of classic LSW theory or in terms of the migration of grain boundary liquid films. These analyses suggest that the coarsening rate should increase with increasing solid fraction, f_S, but this suggestion conflicts with previous experimental results which show that coarsening rate decreases with increasing f_S for f_S>0.7. This paper shows, for the first time, that coarsening rate does increase with f_S for f_S less than approximately 0.75 in agreement with the liquid film migration model, and then decreases again with further increasing f_S for f_S greater than approximately 0.75. A modified model of liquid film migration is proposed which takes into account the reducing area of the liquid film as f_S increases for high f_S. The formation of intragranular liquid droplets, and the pinning of grain boundary liquid films by dispersoids during coarsening are also discussed.