This chapter focuses on the connected speech processes that specifically change the realisation of individual vowels and consonants in particular. It covers the basic concepts related to connected speech processes and discusses the limited literature that is available to talk about whether these connected speech processes occur or do not occur in varieties of English outside of the Inner Circle. The chapter discusses the implications for English as an international language (EIL) pronunciation teaching. It presents the connected speech processes in the EIL classroom not for the purpose of non-native speakers accommodating towards native English speech patterns but in order for non-native speakers to be able to fully comprehend native English speech. The main reason motivating the type of connected speech processes that occur to be because the speaker needs to take articulatory shortcuts and the purpose of the shortcuts is to be able to produce the sound segments with articulatory ease.