A rheological model of stress relaxation in a thin lubricant film, which is formed on the friction surface under the influence of the force field of the friction surface in the presence of fullerene compositions in lubricants, was developed. Analysis of the model made it possible to establish that the existence of elastic or viscous properties in surface structures depends on the ratio of two parameters. This is the time of stress relaxation in the structure on spots of actual contact and the duration of stress action on these spots, which is termed the lifetime of an actual contact spot. It was shown that an increase in the sliding rate reduces the time of relaxation of stresses in the surface structure. This is due to the destruction of aggregates in the structure of gel and the appearance of rotational movements of separate units ‒ flocs. An increase in the load on the tribosystem significantly increases the value of relaxation time. This is due to squeezing the viscous component out of the structure of a surface film. It was established that if the relaxation time exceeds the duration of actions of stresses on actual contact spots, the structure of a surface film behaves like an elastic solid. Conversely, if relaxation time becomes shorter than the duration of stress action, the film behaves like a viscous medium. Theoretically, it was shown that in the range of sliding and loading rates, when a film behaves like an elastic solid, a decrease in stresses on actual contact spots does not exceed the values of 1.1‒22.8 %. This property provides the bearing capacity of a film. The development of the model will make it possible to simulate elastic and viscous properties of "stitched" structures and substantiate the rational concentrations of additives to lubricants, as well as the ranges of their use.