In this paper, I propose to interpret the history of stability analysis of a Walrasian exchange economy through the lenses of the concept of substitutability. A purely mathematical approach of this story does not seem sufficient to account for the way economists have studied the question of stability and how thay have reacted to the results of this research program. My point is that mathematical constraints kept apart, the concept of substituability has shaped the path followed by stability analysis since the publication of Value and Capital (Hicks, 1939) up to the Sonnenschein-Mantel-Debreu theorems and beyond. Thus, I uphold that firstly, the concept of substitutability allows to catch the heuristic behind the work on stability, and secondly, it allows replacing the importance of SMD results in a broader context, giving a more subtle view of the ups and down of general equilibrium theory as a research program.