The cyclic application of grammatical operations has been part of the generative enterprise from the very beginning, when syntax was first defined as “the study of the principles and processes by which sentences are constructed in particular languages”, thereby determining linguistic structure. In its initial formulation (Chomsky, Halle and Lukoff 1956), the cycle was stipulated as part of a phonological rule that assigned stress to phonological representations of English words and phrases. In the work that followed, culminating in The Sound Pattern of English (Chomsky and Halle 1968), it was assumed that a cyclic principle governed the application of rules of the phonological component, which led to a simplification of those rules as well as a shift in focus from the formulation of language-specific processes to general principles governing the application of rules. Extending the principle of cyclic application to the rules of syntax was achieved by a major reformulation of syntactic processes—namely, the introduction of clausal recursion in phrase structure rules (Chomsky 1965). Coinciding with the introduction of trace theory, the cyclic principle was sharpened to the Strict Cycle Condition (SCC, Chomsky 1973). It was then demonstrated that the empirical effects of this condition could be derived via independently motivated general principles under trace theory (Freidin 1978). In the Minimalist Program, the SCC is reformulated as an extension condition on structure building operations (Chomsky 1992), reduced to the operations Merge and Move (Chomsky 1995)—ultimately a single operation Merge (Chomsky 2004). This extension condition is, in effect, subsumed under a more general third factor condition on efficient computation, the No Tampering Condition (Chomsky 2005). The final section of this paper examines the most recent formulation of Merge as an operation on/within a workspace and attempts to demonstrate how restricting that formulation imposes cyclicity on derivations. The cyclic application of rules in generative grammar, which begins as a stipulation in the formulation of a single rule for English stress assignment, becomes a general principle of UG in a shift of focus from processes to principles that govern their application. In the Minimalist Program, cyclicity is ultimately construed as the result of third factor principles of efficient computation, another shift in focus from language-specific UG to principles of computation in general. The discussion of the last section of this paper proposes that cyclicity might actually follow from the formulation of Merge, thus returning to a focus on processes and raising interesting questions about the relation between principles and processes and their interaction with third factor considerations of computational efficiency—leading to a stronger formulation of the Strong Minimalist Thesis.