Nonconforming finite element discretisations require special care in the construction of the prolongation andrestrictioninthemultigridprocess. Inthispaper,ageneralschemeisproposed,whichguaranteesthe approximation property. As an example, the technique is applied to the discretisationby non-matching grids (mortar elements). AMS Subject Classifications: 65F10, 65N55, 65N30. Key Words: Nonconforming finite element method, mortar, multigrid method.