The Rossi X‐ray Timing Explorer (RXTE) has demonstrated that the dynamical variation of the X‐ray emission from accreting neutron stars and stellar mass black holes is a powerful probe of their strong gravitational fields. At the same time, the X‐ray burst oscillations at the neutron star spin frequency have been used to set important constraints on the mass and radius of neutron stars, hence on the equation of state of their high density cores. The X‐ray Evolving Universe Spectroscopy mission (XEUS), the potential follow‐on mission to XMM‐Newton, will have a mirror aperture more than ten times larger than the effective area of the RXTE proportional counter array (PCA). Combined with a small dedicated fast X‐ray timing detector in the focal plane (XTRA: XEUS Timing for Relativistic Astrophysics), this collecting area will provide a leap in timing sensitivity by more than one order of magnitude over the PCA for bright sources, and will open a brand new window on faint X‐ray sources, owing to the negligible detector background. The use of advanced Silicon drift chambers will further improve the energy resolution by a factor of ∼ 6 over the PCA, so that spectroscopic diagnostics of the strong field region, such as the relativistically broadened Iron line, will become exploitable. By combining fast X‐ray timing and spectroscopy, XTRA will thus provide the first real opportunity to test general relativity in the strong gravity field regime and to constrain with unprecedented accuracy the equation of state of matter at supranuclear density. © 2004 American Institute of Physics