Abstract: In a guiding device for mechanical members, which consists of two parts intended to engage by sliding friction, one of the two parts, called the smooth part, has a smooth, functional, i.e. friction, surface and the other part, called the pierced part, has at least one functional, i.e. friction, surface, including emergent cavities intended to accommodate a grease of the lubricating-paste type and especially an EP grease (extreme-pressure grease) comprising a soap-type constituent, an oil-type constituent and an extreme-pressure additive. The contact angle &thgr; between the functional surface of the smooth part and the grease is in the range from 20 degrees to 40 degrees and the material of the pierced part is such that the contact angle between the functional surface of the pierced part and the grease is in the range from 45 degrees to 75 degrees. The device may be of the slideway/runner type, shaft/bearing type, ball/socket joint type, etc.