A new model of parallel computation, namely the FIFO nets is introduced. After giving some basic definitions, it is recalled that it is possible to simulate effectively Petri nets and coloured Petri nets. In addition, one abbreviation is given, increasing the descriptive power of the model of parallel computation. Then it is shown how a class of FIFO nets, the alphabetic FIFO nets, can simulate a program machine. By this way, it is proved that FIFO nets have the same algorithmic power as a Turing machine.