The present study acts upon Rivers' (1971 and 1972) urgings to base second language listening instruction on both psychological and linguistic findings and, at the same time, contends that advanced second language students' listening needs call for improvement in processing spoken discourse. Psychological data on memory span is cited to demonstrate that advanced second language students differ from intermediate second language students and from native speakers in processing capacity of a particular type. Linguistic discourse analysis findings are cited to demonstrate the types of clues and continuities second language listeners must attend to if they are to adequately comprehend spoken discourse. A three‐phase approach to listening instruction and practice for advanced second language students is proposed to meet their discourse processing needs; English, as the target language, is discussed as the case in point. Phase One consists of practice aimed toward increasing students' familiarity with and accuracy in processing intrasentential items and thus toward reducing the processing time devoted to intrasentential items. Phase Two pushed students to expand the time they have left over for processing discourse relations by requiring them to perform operations beyond those necessary for processing individual sentences. Phase Three consists of instruction in the types of discourse clues and continuities available to listeners and practice in attending to such clues and continuitie