By a multiperiodic composite we mean a composite solid in which all constituents are periodically distributed in a matrix but a representative element (unit cell) may not exist. The aim of this Note is to propose a nonasymptotic approach to the formation of averaged (macroscopic) models of multiperiodic composites. The approach is based on the concept of tolerance averaging, which in [2] was applied to the modelling of periodic composites. The derived model, in contrast to homogenization, describes the effect of microstructure size on the overall solid behaviour and yields necessary conditions for the physical correctness of solutions to special problems. To cite this article: C. Woźniak, C. R. Mecanique 330 (2002) 267–272.