The supporting and attaching device is connected to non-rotating parts of at least one brake caliper or yoke intended to cooperate with a brake disk and it comprises an attaching piece in a generally arcuate form, situated beyond the periphery of the disk and of which at least part of the transversal section is U-shaped with two legs one of which legs constitutes the section of a plate clamped onto a single arm for wheel suspension, while the other leg constitutes the section of at least one tab secured on either side to a brake caliper straddling a brake disk and is applied to double disk brakes for motorcycles.