1. An interface device for a computer system comprising at least one master working with at least one slave adapted to be readable and writable at chosen addresses, each master being adapted to execute tasks and to deliver slave addresses for reading and/or writing purposes, characterized in that it comprises a group of first FIFO memories each assigned to one of said masters for storing data representative of their executed tasks, a group of dynamically allocatable second FIFO memories linkable to one another and to said first FIFO memories and processing means arranged to compute dynamically a FIFO memory size required by each of said masters at a given time, considering the tasks it is executing, and to allocate dynamically a number of second FIFO memories to each of said masters chosen according to the corresponding computed FIFO memory size.