This thesis investigates the factors that determine whether complements marked in the subcategorization of verbs are obligatory or optional. The model used is that of Chomsky (1965). In 1.1, the notion of verbal complement is defined and is limited to direct objects, indirect objects, prepositional objects, directionals and some locatives; 1.2, consists largely of a resume of past discussions that have a bearing on the main topic of this investigation. It emerges that a distinction must be drawn between the absence of unspecified and specified complements. Chapter 2 deals with the omission of unspecified complements, 3 with the omission of specified complements that consist of simple noun phrases. Chapter 4 opens with a discussion of the status of sentential complements and the structure of sentences containing such complements; the rest of the chapter deals with the omission of the various types of sentential complements. Chapter 5 deals with the omission of reflexive and reciprocal pronouns. Chapter 6 discusses how the phenomena described in Chapters 2--5 should be handled by a grammar. The conclusion is reached that verbs that can be used without specified complements should be subcategorized as taking optional complements, so that there is no need to account for the absence of unspecified complements by a deletion transformation. Such a transformation is, however, necessary to account for the absence of specified complements. The main body of the thesis is followed by three Appendixes