The scope of this work is certain linguistic elements which make no contribution towards the truth-conditional content of their utterances. Nevertheless, they play a crucial role in utterance interpretation. They function as constraints on the inferential computations the hearer performs in order to establish the relevance of the proposition in which they occur. The sort of expressions this work is concerned with are items like so, after all, you see, llowever and although in both English and their counterparts in the Syrian dialect of the Arabic language spoken in two cities, Lattakia and Homs. The framework of this study is supplied by Sperber and wilson who argue that relevance is the key to communication. This relevance-based framework is adopted by Blakemore (1987) in terms of whose ideas the English and the Syrian Arabic expressions are analysed as semantic constraints on relevance. The concept of a "discourse connective" adopted in this study differs greatly from those discourse analysts who use this term in a broader sense. In this study the term "discourse connective" is reserved for those expressions whose function is not to contribute to the truth-conditional content of their utterances rather to indicate how the interpretation of one utterance contributes to the interpretation of the other. As one expects similarities and differences between the English expressions and their Syrian counterparts arise but the similarities are much greater than the differences.