Abstract : This thesis aims at making effective some theorems and at implemeting efficiently some algorithms in differential algebra in order to apply them to the nonlinear control theory. We present three original results. The first one is an algorithm, Rosenfeld-Gröbner, which describes the models of a polynomial system of equations and inequations in differential algebra (ordinary or with partial derivatives). The algorithm solves the emptyness problem hence the membership problem to radicals of finitely generated differential ideals. Our second result is a method which computes the characteristic set of a prime differential ideal given by a generating family. We last give some new proofs for Seidenberg's elimination algorithms. The algorithms that we describe are effective: they only rely on addition, multiplication, derivations and the the equality to zero test in the base field of the equations.