Detailed molecular dynamics (MD) studies of the origin of medium-range order in the liquid and glassy phases of alloys are presented. Particular attention is devoted to the investigation of finite-size and self-averaging effects. It is shown that already in the liquid phase the preferred Ni - B bonding leads to the formation of B-enriched regions with the approximate stoichiometry of the crystalline compounds and correlation lengths of 10 to 20 Å. If the MD simulations are performed for ensembles of medium size (1000 to 1500 atoms) where the diameter of the MD cell is not much larger than the correlation length, the amplitude of the long-wavelength concentration fluctuations continues to oscillate even after very long runs ( steps). No such oscillations are observed in much larger ensembles ( atoms). Pair correlation functions and static structure factors obtained in both simulations are in good agreement if the time averages over the smaller ensemble cover several periods of the oscillations in the concentration fluctuations. The effects of these oscillations on simulated quench experiments for the glassy phase are discussed and it is shown that good agreement with small-angle diffraction experiments can be achieved.