A zircon separate from a syenite from the Florida Mountains, near Deming, southwest New Mexico, yields a 514 +/- 3- Ma concordia upper-intercept age. However, Rb-Sr isochron dates from syenite and other igneous core rocks in the Florida Mountains range from approximately 519 to approximately 381 Ma. The Rb-Sr dates are based on scattered linear arrays suggestive of open-system conditions for the rocks. Calculated initial Sr-87/Sr-86 ratios are highly variable for presumably coeval rocks, and some are anomalous values below 0.699. K-Ar dates from these igneous core rocks range from 555 to 418 Ma, while an andesite dike, possible associated with tertiary mineralization in the area, yields a date of 27.9 Ma. The zircon U-Pb concordia age can be reconciled with the available stratigraphic controls that require a pre-Middle-Ordovician age for some granite and syenite core-rock exposures. Collectively, the geochronologic data argue for Early Paleozoic plutonism at approximately 550-510 Ma, with a resetting event affecting the Rb-Sr and K-Ar systematics in the syenite and alkali granite in the Tertiary. The resetting mechanism may have involved Sr loss, possibly through ion-exchange reactions between feldspar and moderately heated fluids, as well as loss of Ar and/or addition of K in the syenites, alteration of the Th/U ratio in the syenite and granite, and production of brick-red K-feldspars due to the incorporation of minute hematitic inclusions. Delta-O-18-values for several whole-rock samples range between + 5.8 and + 9.2%, consistent with a high water/rock ratio and alteration temperatures of less-than-or-equal-to 300-degrees-C. World-wide, red-rock granophyre terranes commonly yield discordant Rb-Sr and U-Pb dates, with Rb-Sr dates scattered and systematically younger than U-Pb ages. We suggest that red-rock granophyres are inherently undatable by the Rb-Sr technique because of Sr loss from K-feldspars during penetration of Fe-oxidizing solutions.