  In this paper we set up a general Kolyvagin system machinery for Euler
systems of rank r (in the sense of Perrin-Riou) associated to a large class of
Galois representations, building on our previous work on Kolyvagin systems of
Rubin-Stark units and generalizing the results of Kato, Rubin and Perrin-Riou.
Our machinery produces a bound on the size of the classical Selmer group
attached to a Galoys representation T (that satisfies certain technical
hypotheses) in terms of a certain r \times r determinant; a bound which
remarkably goes hand in hand with Bloch-Kato conjectures. At the end, we
present an application based on a conjecture of Perrin-Riou on p-adic
L-functions, which lends further evidence to Bloch-Kato conjectures.
