The English auxiliary system exhibits many lexical exceptions and subregularities, and considerable dialectal variation, all of which are frequently omitted from generative analyses and discussions. This paper presents a detailed, movement-free account of the English Auxiliary System within Sign-Based Construction Grammar (Sag 2010, Michaelis 2011, Boas & Sag 2012) that utilizes techniques of lexicalist and construction-based analysis. The resulting conception of linguistic knowledge involves constraints that license hierarchical structures directly (as in context-free grammar), rather than by appeal to mappings over such structures. This allows English auxiliaries to be modeled as a class of verbs whose behavior is governed by general and class-specific constraints. Central to this account is a novel use of the feature aux, which is set both constructionally and lexically, allowing for a complex interplay between various grammatical constraints that captures a wide range of exceptional patterns, most notably the vexing distribution of unstressed do, and the fact that Ellipsis can interact with other aspects of the analysis to produce the feeding and blocking relations that are needed to generate the complex facts of EAS. The present approach, superior both descriptively and theoretically to existing transformational approaches, also serves to undermine views of the biology of language and acquisition such as Berwick et al. (2011), which are centered on mappings that manipulate hierarchical phrase structures in a structure-dependent fashion.