The passage of a container along a conveyor is lubricated by applying to the container or conveyor a phase-separating mixture of a hydrophilic lubricating material and an oleophilic lubricating material whose specific gravity is less than or equal to the specific gravity of the hydrophilic lubricating material. Prior to being applied to the container or conveyor, the mixture is agitated or otherwise maintained in a mixed but unstable state. Following application, the hydrophilic lubricating material and oleophilic lubricating material tend to undergo phase-separation, with the oleophilic lubricating material typically forming a film atop the hydrophilic lubricating material, thereby providing a water-repelling lubricating layer having reduced water sensitivity. The mixture can be applied in relatively low amounts and with relatively low or no water content, to provide thin, substantially non-dripping lubricating films. In contrast to dilute aqueous lubricants, the lubricants of the invention provide drier lubrication of the conveyors and containers, a cleaner conveyor line and reduced lubricant usage, thereby reducing waste, cleanup and disposal problems.