Context : The \alpha Centauri binary system , owing to its duplicity , proximity and brightness , and its components ’ likeness to the Sun , is a fundamental calibrating object for the theory of stellar structure and evolution and the determination of stellar atmospheric parameters . This role , however , is hindered by a considerable disagreement in the published analyses of its atmospheric parameters and abundances . Aims : We report a new spectroscopic analysis of both components of the \alpha Centauri binary system , compare published analyses of the system , and attempt to quantify the discrepancies still extant in the determinations of the atmospheric parameters and abundances of these stars . Methods : The analysis is differential with respect to the Sun , based on spectra with R = 35 000 and signal-to-noise ratio \geq 1 000 , and employed spectroscopic and photometric methods to obtain as many independent T _ { eff } determinations as possible . The atmospheric parameters are also checked for consistency against the results of the dynamical analysis and the positions of the components in a theoretical HR diagram . Results : The spectroscopic atmospheric parameters of the system are found to be T _ { eff } = ( 5847 \pm 27 ) K , [ Fe/H ] = + 0.24 \pm 0.03 , \log g = 4.34 \pm 0.12 and \xi _ { t } = 1.46 \pm 0.03 km s ^ { -1 } , for \alpha Cen A , and T _ { eff } = ( 5316 \pm 28 ) K , [ Fe/H ] = + 0.25 \pm 0.04 , \log g = 4.44 \pm 0.15 and \xi _ { t } = 1.28 \pm 0.15 km s ^ { -1 } for \alpha Cen B . The parameters were derived from the simultaneous excitation & ionization equilibria of Fe i and Fe ii lines . T _ { eff } s were also obtained by fitting theoretical profiles to the H \alpha line and from photometric calibrations . Conclusions : Good agreement was reached between the three criteria for \alpha Cen A . For \alpha Cen B the spectroscopic T _ { eff } is \sim 140 K higher than the other two determinations . We discuss possible origins of this inconsistency , concluding that the presence of NLTE effects is a probable candidate , but we note that there is as yet no consensus on the existence and cause of an offset between the spectroscopic and photometric T _ { eff } scales of cool dwarfs . The spectroscopic surface gravities also agree with those derived from directly measured masses and radii . An average of three independent T _ { eff } criteria leads to T _ { eff } ( A ) = ( 5824 \pm 26 ) K and T _ { eff } ( B ) = ( 5223 \pm 62 ) K. The abundances of Na , Mg , Si , Mn , Co and Ni and , possibly , Cu are significantly enriched in the system , which also seems to be deficient in Y and Ba . This abundance pattern can be deemed normal in the context of recent data on metal-rich stars . The position of \alpha Cen A in an up-to-date theoretical evolutionary diagrams yields a good match of the evolutionary mass and age ( in the 4.5 to 5.3 Gyr range ) of with those from the dynamical solution and seismology , but only marginal agreement for \alpha Cen B , taking into account its more uncertain T _ { eff } .