Pursuing the program launched our previous works [Numer. Math. 99 (2005), 411-440] and [SIAM J. Sci. Comput. 27 (2005), 914-936], we propose a relaxation scheme for the numerical simulation of one-dimensional two-phase multi-component flows governed by a drift-flux model, the main features of which are a large number of components and a high degree of nonlinearity in the closure laws. In the explicit setting, the relaxation approach allows to ensure positivity for the densities and the mass fractions. The relaxation method is worked out further so as to fit into a hybrid explicit-implicit setting, where fast acoustic waves are treated implicitly to save computational time while slow kinematic waves are treated explicitly in order to maintain accuracy on the transportation of materials.