Be stars are rapidly spinning B stars surrounded by an outflowing disc of gas in Keplerian rotation . Be star/X-ray binary systems contain a Be star and a neutron star . They are found to have non-zero eccentricities and there is evidence that some systems have a misalignment between the spin axis of the star and the spin axis of the binary orbit . The eccentricities in these systems are be caused by a kick to the neutron star during the supernova that formed it . Such kicks would also give rise to misalignments . In this paper we investigate the extent to which the same kick distribution can give rise to both the observed eccentricity distribution and the observed misalignments . We find that a Maxwellian distribution of velocity kicks with a low velocity dispersion , \sigma _ { k } \approx 15 km s ^ { -1 } , is consistent with the observed eccentricity distribution but is hard to reconcile with the observed misalignments , typically i \geq 25 ^ { \circ } . Alternatively a higher velocity kick distribution , \sigma _ { k } = 265 km s ^ { -1 } , is consistent with the observed misalignments but not with the observed eccentricities , unless post-supernova circularisation of the binary orbits has taken place . We discuss briefly how this might be achieved .