Problems of inquiry in intercultural communication are examined in this paper, and an inquiry process is presented that can be applied to the study of communication between people from different cultures. The first section of the paper outlines major, well-documented procedural problems in intercultural communication and considers additional problems under two headings: structural and substantive. The second section discusses the general nature of the process of inquiry and outlines each of four phases in this process: observing, discovering, theorizing, and verifying. It then examines four additional phases, considered to be the joint applications of the four basic phases (empirical generalization, theory construction, theory evaluation, and empirical confirmation), shows the interrelationship of all the phases and the cyclical nature of the inquiry process, and presents a set of principles for mastering and applying the "cross fertilization" of inquiry phases. The final section of the paper discusses implications of the scientific inquiry process and its phases for the study of intercultural communication. (GT)