are closer to the biologic vision of the tissue and allow to study motion and dynamics of the tissue. This paper aims to extend the link between the mechanical and the free boundary models, in the case of multiple populations system.

In the specific case of multiple populations, several mathematical models have been already introduced. In particular in population dynamics, the famous Lotka-Volterra system [@Lotka] models the dynamics of a predator-prey system. This model has been extended to nonlinear diffusion Lotka-Volterra systems [@BERTSCH198756; @B1987; @BGHP; @BT]. For the tumor growth modelling (see e.g. [@CGP]), some models focus on mechanical property of tissues such as contact inhibition [@BHIM; @BPM; @GSV] and mutation [@GALIANO]. They have been extended to multiple populations [@GALIANO; @SHIGESADA197983]. Solutions to these models may have some interesting spatial pattern known as segregation [@BGHP; @CarilloSchmidtchen; @Mimura1980; @SHIGESADA197983].

The two cell populations system under investigation in this paper is an extension on a simplest cell population model proposed in [@BD; @PQV]. Let $n(x,t)$ be the density of a single category of cell depending on the position $x \in \RR^d$ and the time $t>0$, and let $p(x,t)$ be the mechanical pressure of the system. The pressure is generated by the cell 