In this talk,  I will talk about a singular limit problem for a compressible one-velocity bifluid system, which is based on a joint work with  C. Burtea and T. Crin-Barat.

I will show rigorously that the so-called Kapila system is obtained as a pressure-relaxation limit from the so-called Baer-Nunziato (BN) system when the relaxation parameter tends to zero. A stability estimate between these two systems will also be presented.