  We present a new first-principles theory of dynamic arrest in colloidal
mixtures based on the multi-component self-consistent generalized Langevin
equation (SCGLE) theory of colloid dynamics [Phys. Rev. E {\bf 72}, 031107
(2005); ibid {\bf 76}, 039902 (2007)]. We illustrate its application with the
description of dynamic arrest in two simple model colloidal mixtures, namely,
the hard-sphere and the repulsive Yukawa binary mixtures. Our results include
the observation of the two patterns of dynamic arrest, one in which both
species become simultaneously arrested, and the other involving the sequential
arrest of the two species. The latter case gives rise to mixed states in which
one species is arrested while the other species remains mobile. We also derive
the ("fixed point") equations for the non-ergodic parameters of the system,
which takes the surprisingly simple form of a system of coupled equations for
the localization length of the particles of each species. The solution of this
system of equations indicates unambiguously which species is arrested (finite
localization length) and which species remains ergodic (infinite localization
length). As a result, we are able to draw the entire ergodic--non-ergodic phase
diagram of the binary hard-sphere mixture.
