Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic transition-metal carbides TiC and TaC as functions of temperature in the range 135-295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The carbon concentration of each ceramic has been determined using an oxidation method: the carbon-to-metal atomic ratios are both 0.98. In general, the values determined for the adiabatic bulk modulus (B-S), shear stiffness (mu), Young's modulus (E), Poisson's ratio (sigma) and acoustic Debye temperature (Theta(D)) for the TiC and TaC ceramics agree well with the experimental values determined previously. The temperature dependences of the longitudinal stiffness (C-L) and shear stiffness measured for both ceramics show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. Both the bulk and Young's moduli of the ceramics increase with decreasing temperature and do not show any unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters. The values determined at 295 K for the hydrostatic pressure derivatives (partial derivativeC(L)/partial derivativeP)(P=0), (partial derivativemu/partial derivativeP)(P=0) and (partial derivativeB(S)/partial derivativeP)(P=0) for TiC and TaC ceramics are positive and typical for a stiff solid. The adiabatic bulk modulus BS and its hydrostatic pressure derivative (partial derivativeB(S)/partial derivativeP)(P=0) of TiC are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (gamma(L)), shear (gamma(S)) and mean (gamma(el)) acoustic-mode Gruneisen parameters of TiC and TaC ceramics are positive: the zone-centre acoustic phonons stiffen under pressure. The shear gamma(s) is much smaller than the longitudinal gamma(L). The relatively larger values estimated for the thermal Gruneisen parameter gamma(th) in comparison to gamma(el) for the TiC and TaC ceramics indicate that the optical phonons have larger Gruneisen parameters. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiC and TaC. (C) 2003 Kluwer Academic Publishers.