Using a first-principles pseudopotential method we have compared the adsorption and dissociation of the common n-type dopant molecule PH3 on the Si(001)-(21) and Ge(001){(21) surfaces. We find that the dissociated state is energetically more favourable than the molecular state by 1.70(0.81) eV, whereas the latter is 0.58(0.25) eV more stable than the system composed of the free silicon(germanium) surface and PH3(g). The chemisorbed system is characterised by elongated Si{Si(Ge{Ge) dimers that are symmetric in the dissociative case and asymmetric in the molecular case and by the fact that the Si(Ge){PH2 as well as the PH3(ads) groups retain the pyramidal geometry of the phosphine molecule. Our dissociative adsorption model is further supported by our calculated vibrational modes, which are in good agreement with available experimental works.