Multiphase mechanical models are now commonly used to describe living tissues
including tumour growth. The specific model we study here consists of two
equations of mixed parabolic and hyperbolic type which extend the standard
compressible porous medium equation, including cross-reaction terms. We study
the incompressible limit, when the pressure becomes stiff, which generates a
free boundary problem. We establish the complementarity relation and also a
segregation result. Several major mathematical difficulties arise in the two
species case. Firstly, the system structure makes comparison principles fail.
Secondly, segregation and internal layers limit the regularity available on
some quantities to BV. Thirdly, the Aronson-B{\'e}nilan estimates cannot be
established in our context. We are lead, as it is classical, to add correction
terms. This procedure requires technical manipulations based on BV estimates
only valid in one space dimension. Another novelty is to establish an L1
version in place of the standard upper bound
