When a laser pulse hits a solid surface with relativistic intensities, XUV attosecond pulses are generated in the reflected light. We present an experimental and theoretical study of the temporal properties of attosecond pulse trains in this regime. The recorded harmonic spectra show distinct fine structures which can be explained by a varying temporal pulse spacing that can be controlled by the laser contrast. The pulse spacing is directly related to the cycle-averaged motion of the reflecting surface. Thus the harmonic spectrum contains information on the relativistic plasma dynamics.