The alpha-relaxation dynamics in a hard-sphere system is studied solving microscopic-mode-coupling equations. The solutions for coherent and incoherent dynamical structure factors, the transversal correlation functions, and the moduli are presented for all wave vectors. The wave-vector dependence of fitted Kohlrausch exponents-beta and of the relaxation times tau is discussed. Recent experiments on the a relaxation of colloidal systems are quantitatively analyzed.