In order to make computers easier to use and more versatile many system designers are exploring the use of multiple windows on a single screen and multiple coordinated screens in a single work station displaying linked or related information. The designers of such systems attempt to take into account the characteristics of the human user and the structure of the tasks to be performed. Central to this design issue is the way in which the user views and cognitively processes information presented in the windows or in multiple screens. This paper develops a theory of the "cognitive layout" of information presented in multiple windows or screens. It is assumed that users adopt a cognitive representation or layout of the type of information to be presented and the relationships among the window of screens and the information they contain. A number of cognitive layouts are derived from theories in cognitive psychology and are discussed in terms of the intent of the software driving the system and congruence with the cognitive processing of the information. It is hypothesized that the particular layout adopted by a user will drastically affect the user's understanding and expectation of events at the human-computer interface and could either greatly facilitate or frustrate the interaction. Ways of ensuring the former and avoiding the latter are discussed in terms of implementations on existing multiple-window and multiple-screen systems.