The spectral evolution of the peculiar SN Ic 2002ap during the first 40 days is presented. The spectra display very broad absorption features, which are typical of hypernovae. The maximum expansion velocity measured on the earliest spectra exceeds 3 times 10^4 km s^{-1}. The spectrum of SN 2002ap at the epoch of maximum brightness resembles that of SN 1997ef more than that of SN 1998bw. The spectral evolution of SN 2002ap proceeds at about 1.5 times the rate of SN 1997ef. The parameterized supernova spectrum synthesis code SYNOW was used to perform line identification and deduce velocity information from the early-phase spectra, which are heavily affected by line blending. The photospheric velocity, as deduced from the fitting results and from the blueshift of the ion{Si}{2} lambda 6355 absorption minimum, is lower than in previously studied hypernovae. At advanced epochs, the ion{Si}{2} lambda 6355 absorption minimum becomes difficult to distinguish. This may be caused by the growth of [ion{O}{1}] lambda lambda 6300, 6364 emission. Together with the rapid spectral evolution, this suggests that SN 2002ap should enter the nebular phase sooner than previously studied hypernovae.
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