A device for guiding mechanical members, which consists of two parts intended to interact by sliding friction, one of the two parts, called the smooth part, having a smooth, functional, i.e. friction, surface and the other part, called the pierced part, having at least one functional, i.e. friction, surface, including emergent cavities intended to accommodate a grease of the lubricating-paste type comprising a soap-type constituent, an oil-type constituent and an extreme-pressure additive, wherein the contact angle θ between said functional surface of said smooth part and said grease, measured at a temperature called the measurement temperature, which is 15°+5° C. below the temperature at which the onset of separation between said soap-type constituent and said oil-type constituent occurs, is in the range from 20 degrees to 40 degrees and the material of said pierced part is such that the contact angle, measured at said measurement temperature, between said functional surface of the pierced part and said grease is in the range from 45 degrees to 75 degrees.