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In this paper we extend Fischler's quantitative generalization ofNesterenko's linear independence criterion, by weakening the hypotheses on thedivisors of the coe cients of the linear forms and allowing (to some extent)the linear forms not to tend to 0. Another version of this result is proved, inthe spirit of Siegel's criterion, with a recurrence relation veri ed by thelinear forms. Finally, the results are restated in a more general setting interms of convex bodies and lattices of $\mathbb{R}^n$.

G\'en\'eralisations Quantitatives du Crit\'ere D'ind\'ependance Lin\'eaire De Nesterenko