  We address the problem of the stability of the computations of resultants and
subresultants of polynomials defined over complete discrete valuation rings
(e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms
are highly unstable on average and we explain, in many cases, how one can
stabilize them without sacrifying the complexity. On the way, we completely
determine the distribution of the valuation of the principal subresultants of
two random monic p-adic polynomials having the same degree.
