This paper discusses the consequences of allowing discontinuous constituents in syntactic representions and phrase-structure rules, and the resulting complications for a standard parser of phrase-structure grammar. It is argued, first, that discontinuous constituents seem inevitable in a phrase-structure grammar which is acceptable from a semantic point of view. It is shown that tree-like constituent structures with discontinuities can be given a precise definition which makes them just as acceptable for syntactic representation as ordinary trees. However, the formulation of phrase-structure rules that generate such structures entails quite intricate problems. .