In this paper we consider the problem of the use of approximate arithmetics in Grobner basis computation. This is useful to reduce the cost of integer arithmetic, but is especially necessary for overdetermined systems whose coefficients are only approximately known.We report on some numerical experiments, that show that the intrinsic instability of the problem is high but not such as to make the problem unmanageable, and that there is space to improve the numerical stability of the algorithms.We suggest some algorithms to deal with the case of overdetermined and unstable systems.