Modality is a cross-linguistic category that is normally discussed in the context of tense and aspect since these three categories are often marked within the verbal complex. Its status, compared with that of tense and aspect, is, however, more vague and complex to the extent that one might find it quite difficult to identify the borderlines of its domain. The thesis attempts to lessen some of this vagueness through studying modality in English and Arabic, from both a descriptive and an analytic perspective. The analysis will draw on the theory of HPSG. The thesis, in general, attempts to achieve five aims. The first is to reduce the obscurity around modality by illustrating its main aspects in general and exploring it in two languages which are different in termns of the way they realise it. The second is to describe the morphological, semantic/notional, and syntactic properties of the set of English modal auxiliaries and how the members of this set interact with negation. The third is to present an up-to-date theoretical account that covers the main aspects of English modal auxiliaries, and, most importantly, fills the current gaps in the literature which will be specified in the review of the relevant previous analyses. The fourth aim is to answer the question 'how is modality expressed in Arabic?' and to provide a detailed theory-neutral description of the linguistic properties of the different Arabic modals and how they interact with negation. The fifth and last aim is to propose a theoretical analysis that covers the formal linguistic aspects of Arabic modals. The work done for achieving the latter three aims will include the thesis' original contribution to the knowledge in the field.