While samarium phosphate (Sm2O3)(x)(P2O5)((1-x)) glasses are known to show pronounced long-wavelength acoustic-mode softening, their lanthanum (La2O3)(x)(P2O5)((1-x)) analogues do not. To investigate experimentally this different influence of lanthanide modifiers, a comparative study has been made of the effects of temperature and pressure on the velocities of ultrasonic waves propagated in binary ((La2O3)(x)(P2O5)((1-x)) and (Sm2O3)(x)(P2O5)((1-x))) and ternary ((La2O3)(x)(Sm2O3)(y)(P2O5)((1-x-y))) phosphate glasses with compositions near to that corresponding to the metaphosphate (R(2)O(3))(0.25)(P2O5)(0.75). For each glass the second-order elastic stiffness tensor components C(IJ)(S +)continue to increase down to 10 K in a manner consistent with ultrasonic interactions with two-level systems. Measurements of the effects of hydrostatic pressure on the ultrasonic wave velocities have been used to determine the hydrostatic pressure derivatives (partial derivative C-IJ(S)/partial derivative P)(T,P=O) of the second-order elastic stiffness tensor components and (partial derivative B-O(S)/partial derivative P)(T,P=O) of the bulk modulus B-O(S) at room temperature (293 K). For the ternary glasses (partial derivative C-11(S)/partial derivative P)(T,P=O,) (partial derivative C-44(S)/partial derivative P)(T,P=O) and (partial derivative B-O(S)/partial derivative P)(T,P=O) are small but positive; these glasses stiffen under pressure. Replacement of samarium by lanthanum in the ternary glasses negates the acoustic-mode softening. Possible sources of the different effects of lanthanum and samarium modifiers on the non-linear acoustic properties of metaphosphate glasses are discussed.