The room-temperature Raman spectra of aragonite, magnesite and dolomite have been recorded up to 30 GPa and 25 GPa, respectively and no phase changes were observed during compression, unlike calcite. The effect of temperature on the room-pressure Raman spectra of calcite, aragonite, magnesite and dolomite is reported up to 800-11 00 K. The measured relative pressure.and temperature-shifts of the Raman lines are greater for the lattice modes than for the internal modes of the CO3 groups. These shifts are used to calculate the mode anharmonic parameters of the observed Raman modes; they are negative and their absolute values are smaller (close to 0) for the internal CO3 modes than for the lattice modes (4-17 10(-5) K-1). The temperature shifts of the lattice modes in calcite are considerably larger than those for dolomite and magnesite, and a marked non-linear increase in linewidth is observed above 400-degrees-C for calcite. This is consistent with an increasing relaxational component to the libration of the CO3 groups about their threefold axes, premonitory to the rotational order-disorder transition at higher temperature. This behaviour is not observed for the other calcite structured minerals in this study. We examine systematic variations in the lattice mode frequencies and linewidths with composition, to begin to understand these differences in their anharmonic behaviour. Finally, we have used a simple Debye-Waller model to calculate atomic displacements in calcite, magnesite and dolomite with increasing temperature from the vibrational frequency data, to provide a direct comparison with atomic positional data from high-temperature structure refinements.