In this paper we present BeppoSAX and XMM-Newton observations of two long Gamma-ray bursts, the X-ray rich event of December 11, 2001 (GRB011211) and the hard and very bright event of November 21, 2001 (GRB011121). In both events we find evidence of a late X-ray burst, taking place several minutes after the prompt emission. In the November burst the spectrum of the X-ray burst is much softer th...