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The purpose of this talk is to present some recent progress on the existence theory for a particular type of degenerate cross-diffusion system in one space dimension, which expands on the prior works of Meszaros-Parker and Elbar-Santambrogio. We will discuss a special formulation of the problem which allows us to use monotonicity methods à la Minty-Browder. This is joint work with Filippo Santambrogio.