Abstract Self-diffusion in multi-component glass-forming systems including fragile and strong glasses is studied from a unified viewpoint. A simple analytic form of long-time self-diffusion coefficient D S L is proposed. The equations for the mean-square displacements recently derived for two types of systems, (S) suspensions of colloids and (M) molecular systems, from a first principle by employing the Tokuyama–Mori projection-operator method are used to define D S L in each type formally, both of which are uniquely determined by the correlation function of the fluctuating forces. Analyses of the correlation functions in two types in terms of many-body interactions thus lead in type (M) to D S L ( λ ) ≃ κ − 1 ( λ c / λ ) ( 1 − λ / λ c ) 2 , where λ is a control parameter, such as an inverse temperature and a volume fraction. Here κ is simply written in terms of the potential parameters and λ c an adjustable parameter to be determined. The predictions for λ dependence of D S L in multi-component glass-forming systems are in excellent agreement with available experimental data and simulation results in equilibrium states.