The rare-earth elements (REE; the lanthanides plus Y and Sc) have a wide range of high-tech applications (including in batteries and magnets) that are essential to our society. Monazite, a phosphate mineral containing variable amounts of Ce, La, Nd, Pr and Th, is a common REE ore in carbonatite–alkaline complexes. To better understand the behaviour of monazite in these systems, we investigated the solubility of synthetic Nd-monazite (to avoid complications due to the redox variability of Ce) in nephelinitic compositions containing a large number of trace elements and with carbonate contents between ~6 and ~37 wt. % at 1 GPa and 1100 °C to 1500 °C. In the experiments, the products were monazite crystals ranging in size from several microns at 1100 °C to 50 µm at 1500 °C and glass (occasionally with spinifex silicate crystals). The Nd concentration of the melt determined by electron probe microanalysis varied from ~3.5 wt. % at 1100 °C to ~21.5 wt. % at 1500 °C for a nephelinite containing ~6 wt. % carbonate. The effect of carbonate concentration on the solubility of monazite is being investigated and monazite-melt partition coefficients for trace elements will be determined. The findings of this study could provide insights into the formation of monazite in carbonatite–alkaline complexes that possess unusually high REE contents (up to wt. % levels), for example Mountain Pass in California, USA and Mount Weld, Western Australia.