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An early steep decay component following the prompt GRBs is commonly observedin {\em Swift} XRT light curves, which is regarded as the tail emission of theprompt gamma-rays. Prompted by the observed strong spectral evolution in thetails of GRBs 060218 and 060614, we present a systematic time-resolved spectralanalysis for the {\em Swift} GRB tails detected between 2005 February and 2007January. We select a sample of 44 tails that are bright enough to performtime-resolved spectral analyses. Among them 11 tails are smooth and withoutsuperimposing significant flares, and their spectra have no significanttemporal evolution. We suggest that these tails are dominated by the curvatureeffect of the prompt gamma-rays due to delay of propagation of photons fromlarge angles with respect to the line of sight . More interestingly, 33 tailsshow clear hard-to-soft spectral evolution, with 16 of them being smooth tailsdirectly following the prompt GRBs,while the others being superimposed withlarge flares. We focus on the 16 clean, smooth tails and consider three toymodels to interpret the spectral evolution. The curvature effect of astructured jet and a model invoking superposition of the curvature effect tailand a putative underlying soft emission component cannot explain all the data.The third model, which invokes an evolving exponential spectrum, seems toreproduce both the lightcurve and the spectral evolution of all the bursts,including GRBs 060218 and 060614. More detailed physical models are called forto understand the apparent evolution effect.Comment: 13 pages in emulateapj style,6 figures, 1 table, expanded version,  matched to published version, ApJ, 2007, in press. This is the first paper of  a series. Paper II see arXiv:0705.1373 (ApJ,2007, in press

A Comprehensive Analysis ofSwiftXRT Data. I. Apparent Spectral Evolution of Gamma‐Ray Burst X‐Ray Tails