It is well known that, within certain limits, a quarter-wave plate may be made from two suitably oriented cellophane sheets. An attempt to construct such composite plates showed up some of their interesting peculiarities. These are discussed in the present paper, which also gives constructional details of quarter- and half-wave plates and extends the theory to include two- and three-component wave plates of any delay. General expressions are developed to cover all these cases; in the case of triple-sheet combinations it is shown that it is possible to neutralize the rotation of axes which is unavoidable with two-component plates and to produce composite plates having all the properties of simple plates. To assist the design and assembly of composite plates, tables of constructional constants for double and triple quarter-wave plates, and triple half-wave plates are included.