The linear model of innovation, which assumes a unidirectional and non-simultaneous relationship between the two realms of science and technology, is still a debated framework. The aims of this article are to show—in contrast with the received view—that economists of science in the 1950s and 1960s did not develop or support the linear model, to examine the theoretical and empirical foundations of their representation of the links between science and technology, and to study its consequences for patent policies. To do so, we mainly focus on Richard Nelson’s seminal and recent articles on the economics of science and examine the contributions to the economics of science and invention from authors belonging to Nelson’s network. We show that Nelson developed—as early as the late 1950s and early 1960s—an interactionist representation of the links between science and technology and noted that basic science can also develop with practical objectives. We explain Nelson’s development of an interactionist model by his adoption of an evolutionary approach—represented by circular causality and an emphasis on historical continuity—stemming from the influence of the evolutionary approach on his research carried out at that time at the RAND Corporation and the Carnegie Institute of Technology. We then examine the genealogy of the notion of “technological paradigm” developed in the 1980s and show its links with the contributions to the old economics of science, a criticism of the linear model, and an evolutionary approach. We conclude by showing that Nelson’s recent concerns about patent policies are a consequence of his evolutionary approach and related criticism of the linear model.