We present an analysis of 530 high-resolution spectra of the beta Cephei star epsilon Cen, showing complex variations in the rotationally broadened absorption line-profiles of the SiIII triplet (lambda4552, 4567, 4574 Angstrom). Most data were acquired during four dedicated observing runs between April 1996 and June 1998, with time spans between 6 and 14 days. We calculate velocity moments of the line profiles and apply Fourier analysis techniques to analyze their time behavior. The variations of the velocity moments confirm the presence of two periods already known from photometry, and provide evidence for the presence of two or more non-radial pulsation modes. Our analysis of the spectral time series concentrates on the variability at each position in the lambda 4567 Angstrom line profile. In addition to the two frequencies found in the radial-velocity variations, we find several other periodicities to be present across the line profile. We use Fourier analysis, sinusoid fitting, and folding techniques to analyze the amplitude and phase information for each of the detected periods. We find evidence for at least five pulsation modes in epsilon Cen, and identify l-values between 2 and 5.