This paper studies the nonlinear dependences in daily returns of 40 French stocks and two indices, the Vontobel-Datastream index and the official French index CAC40. These returns are studied during a period of twenty-four years beginning January 1, 1975. The rescaled range analysis of Hurst and the Brock-Dechert-Sheinkman (BDS) test show that the assumption that the stocks and indices returns are independent and identically distributed should be rejected. The analysis of the fractal dimension by regressing the demivariogram function seems however to show that short term and long term dependences have the same characteristics. Returns are then modelized by a GARCH(1,1)-process; the analysis of the residuals by the BDS test show that most part of the dependences are no more significative.