The effect of pressure on the relaxation processes in poly(propylene glycol) of number-average molecular weights 400 and 4000 g mol(-1) (PPG-400 and PPG-4000) has been investigated using dielectric spectroscopy as well as thermal conductivity and heat capacity measurements. The relaxations associated with segmental motions within the polymer chain (alpha relaxation) and whole chain motions (alpha' relaxation) have been studied in the temperature range 200-400 K for pressures up to 2 GPa. The two processes display slightly different sensitivities to pressure, and as a consequence, are better separated at high pressures. As a result, high-pressure data exhibit the alpha' relaxation also in PPG-400, whereas previous investigations at atmospheric pressure have detected it only in PPG of molecular weights above about 1000 g mol(-1). At atmospheric pressure, the values for (partial derivative T/partial derivative p)(tau=1s) of the alpha relaxation are, respectively, 140 and 192 K GPa(-1) for PPG-400 and PPG-4000, where tau is the relaxation time. Because of the difference in (partial derivative T/partial derivative p)(tau), the relaxation of the a motions and therefore the glass-transition temperature exhibits a more significant dependence on molecular weight at high pressures. At 295 K and 0.3 GPa, the activation volumes for the alpha and alpha' processes of PPG-4000 are about the same (approximate to 45 cm(3) mol(-1)). At the same conditions, the activation volume for the a process of PPG-400 is about half of that for PPG-4000. An analysis of the a relaxation in terms of the strong-fragility classification shows that the degree of fragility of both PPG-400 and PPG-4000 increases slightly with increasing pressure.