Lyman transitions of Xe53+∗ produced by nonradiative electron capture in collisions of 95, 146, and 197 MeV/uXe54+ ions with Kr and Xe atoms have been studied experimentally. It shows that the captured electrons preferentially populate lower states. The intensity ratios I(Ly-β)/I(Ly-α) and I(Ly-γ)/I(Ly-α) are found to decrease with increasing projectile velocity, and the ratios for Xe decrease faster than those of Kr. The obtained results are compared with the relative cross sections calculated with the relativistic eikonal approximation. For both targets, the theoretical results overestimate the experimental ratio I(Ly-β)/I(Ly-α) but underestimate I(Ly-γ)/I(Ly-α). Moreover, the theory gives parallel decreasing curves for the two targets, which does not agree with the present experiment. In order to well understand the experimental findings, a more sophisticated theoretical approach is urgently required.