It has been recently proposed a family of rank-one separable potentials (1) which fits the nucleon-nucleon scattering data up to 460 MeV (lab). These potentials were tested in different calculations of two- and three-nucleon parameters. In particular, we mention the fact they reproduce fairly well the off-shell behaviour of the two-nucleon system. As a consequence of these results, it appears interesting to go further with the study of this new set of potentials. It is for this reason that we have investigated their behaviour in connection with nuclear matter.