The skull-bone quadrate in nonavian theropods is very diverse morphologically alongside the disparity of the group as a whole. However this disparity has been underestimated for taxonomic purposes. In order to evaluate the phylogenetic potential and investigate the evolutionary transformations of the quadrate, we conducted a Catalano-Goloboff phylogenetic morphometric analysis as well as a cladistic analysis using 98 discrete quadrate related characters. The cladistic analysis provides a fully resolved tree mirroring to some degree the classification of nonavian theropods. The quadrate morphology by its own provides a wealth of data with strong phylogenetic signal and allows inference of major trends in the evolution of this bone. Important synapomorphies include: for Abelisauroidea, a lateral ramus extending to the ectocondyle; for Tetanurae, the absence of the lateral process; for Spinosauridae, a medial curvature of the ventral part of the pterygoid ramus occurring just above the mandibular articulation; for Avetheropoda, an anterior margin of the pterygoid flange formed by a roughly parabolic margin; and for Tyrannosauroidea, a semi-oval pterygoid flange shape in medial view. The Catalano-Goloboff phylogenetic morphometric analysis reveals two main morphotypes of the mandibular articulation of the quadrate linked to function. The first morphotype, characterized by an anteroposteriorly broad mandibular articulation with two ovoid/subcircular condyles roughly subequal in size, is found in Ceratosauria, Tyrannosauroidea and Oviraptorosauria. This morphotype allows a very weak displacement of the mandible laterally. The second morphotype is characterized by an elongate and anteroposteriorly narrow mandibular articulation and a long and parabolic/sigmoid ectocondyle. Present in Megalosauroidea, Carcharodontosauridae and Dromaeosauridae, this morphotype permits the lower jaw rami to be displaced laterally when the mouth opened.