The present invention relates to a connection system for connecting computer data backup units to a computer motherboard comprising: a support for different sizes of computer data backup units, wherein the backup units carry a connector, or carry a superposition of a plurality of connectors, a multi-stage connector configured to be connected to the motherboard and the backup unit connectors, wherein the multi-stage connector comprises at least two connection stages superposed and fixed to one another. According to the invention, the at least two superposed connection stages of the multi-stage connector are offset relative to one another according to the sense of the connection to the connectors of the computer data backup units carried by the support.