In this paper, we deal with the XRAM model introduced in Cosnard and Ferreira (1991). We show that the original definition of the XRAM model was not accurate enough, and that it must be slightly modified. Thence, we modify the definition of the XRAM model to make it consistent, and we study the consequence of this modification on the complexity theory developed in this model. In particular, the new model modifies the definition of a problem on a XRAM (and thus on a PRAM, and on a RAM since these two models are particular cases of the XRAM). However, we show that, though theoretically important, this modification has no practical consequence on the complexity theory developed on the XRAM model. Only results based on the use of data-movement-intensive problems (Akl et al., 1992) must be carefully reconsidered.