The susceptibility of an experimental nickel-based single-crystal superalloy to the precipitation of topologically close-packed phases (TCPs) is considered. Its composition has been chosen to be enriched with regard to molybdenum with no tungsten being present, in order to promote microstructural instability and to allow this to be studied. Two conditions are examined: (1) as-cast and (2) as-cast with a solutioning and a-ino, treatment. In the as-east condition, it is shown that the interdendritic region is already prone to TCP formation, and that further heat treatment in the vicinity of 1000 degreesC increases the extent of this severely. This is attributed to the partitioning of Ta, which causes an increase in the gamma ' volume fraction in the interdendritic regions and a concomitant enrichment of the gamma matrix with respect to Mo and particularly Cr. In the solutioned and aged state, TCPs form after heat treatment in the range from 800 degreesC to 1100 degreesC and form preferentially at the dendrite cores; this is due to the presence of residual Re, which does not diffuse as quickly as Ta. in the opposite direction. The different TCP particles exhibit very different morphologies. At 1000 degreesC, the P phase is prevalent; around 850 degreesC, the P phase is still found, but mu is predominant and is found in association with sigma. The experimental data are compared with the predictions of thermodynamic software and a database of thermodynamic parameters; the predictions are reasonable, although some discrepancies are noted.