Title: Continuum-Fitting the X-ray Spectra of Tidal Disruption Events Abstract: We develop a general relativistic model to fit the X-ray spectrum after the tidal disruption events (TDEs). we extend time-dependent, general relativistic “slim disk” accretion models to SMBHs. Then we ray-trace the trajectories of photons from the observer to the disk surface, including gravitational redshift, Doppler, and lensing effects self-consistently, producing the first such predictions for the integrated X-ray spectrum from near-horizon scales in TDEs. We have simultaneously and successfully fit the observed, multi-epoch XMM-Newton X-ray data for the two best-sampled X-ray TDEs, ASASSN-14li and ASASSN-15oi. For the former, we fit the spectrum at each epoch assuming that the SMBH mass and spin are constant and letting the accretion rate float. For the latter, for which only two epochs were suited for fitting, we currently assume that the accretion rate follows the fallback rate to predict the spectrum time series. We have also developed a novel explanation, which arises naturally from the evolution of the disk structure itself, for the unexpectedly slow brightening of the ASASSN-15oi in X-rays. For both of these flares, our fitted masses are compatible with estimates from the black hole mass-bulge mass relation in the literature.