A large proportion of computationally-oriented theories of grammar operate within the confines of monostratality (i.e. there is only one level of syntactic analysis), compositionality (i.e. the meaning of an expression is determined by the meanings of its syntactic parts, plus their manner of combination), and adjacency (i.e. the only operation on terminal strings is concatenation). This thesis looks at two major approaches falling within these bounds: that based on phrase structure grammar (e.g. Gazdar), and that based on categorial grammar (e.g. Steedman). The theories are examined with reference to extraction and coordination constructions; crucially a range of 'compound' extraction and coordination phenomena are brought to bear. It is argued that the early phrase structure grammar metarules can characterise operations generating compound phenomena, but in so doing require a categorial-like category system. It is also argued that while categorial grammar contains an adequate category apparatus, Steedman's primitives such as composition do not extend to cover the full range of data. A theory is therefore presented integrating the approaches of Gazdar and Steedman. The central issue as regards processing is derivational equivalence: the grammars under consideration typically generate many semantically equivalent derivations of an expression. This problem is addressed by showing how to axiomatise derivational equivalence, and a parser is presented which employs the axiomatisation to avoid following equivalent paths.