Two developments in the methodology of English teaching have been seen. One is the transition from ELT(English Language Teaching) to ESP(English for Special Purposes)teaching. The other is the transition from linguistic forms and syntactic structures to communicative activities. This essay discusses the classification of ESP/EST, argues for the purpose of ESP/EST teaching and GPE(General Purpose English)teaching. It is then suggested that the characteristics of objectives between ESP/EST and GPE should be differentiated. In the second part, the essay takes as its starting point two kinds of EST courses offered in institutions of higher learning in China. One has the nature of in-service language teaching. The other deals with the EST-majoring programme. The essay seeks to identify what are the main features of the EST-majoring programme, and stresses its practical nature of training and the concern with the learners' communicative competence.