Alzheimer's disease (AD) is characterized by two hallmark molecular pathologies: amyloid aβ and Tau neurofibrillary tangles. To date, studies of functional connectivity MRI (fcMRI) in individuals with preclinical AD have relied on associations with measures of amyloid pathology. With the recent advent of Tau-PET tracers it is now possible to extend investigations on fcMRI in a sample of cognitively normal elderly humans to regional measures of Tau. We modeled fcMRI measures across four major cortical association networks [default-mode network (DMN), salience network (SAL), dorsal attention network, and frontoparietal control network] as a function of global cortical amyloid [Pittsburgh Compound B (PiB)-PET] and regional Tau (AV1451-PET) in entorhinal, inferior temporal (IT), and inferior parietal cortex. Results showed that the interaction term between PiB and IT AV1451 was significantly associated with connectivity in the DMN and salience. The interaction revealed that amyloid-positive (aβ) individuals show increased connectivity in the DMN and salience when neocortical Tau levels are low, whereas aβ individuals demonstrate decreased connectivity in these networks as a function of elevated Tau-PET signal. This pattern suggests a hyperconnectivity phase followed by a hypoconnectivity phase in the course of preclinical AD. This article offers a first look at the relationship between Tau-PET imaging with F-AV1451 and functional connectivity MRI (fcMRI) in the context of amyloid-PET imaging. The results suggest a nonlinear relationship between fcMRI and both Tau-PET and amyloid-PET imaging. The pattern supports recent conjecture that the AD fcMRI trajectory is characterized by periods of both hyperconnectivity and hypoconnectivity. Furthermore, this nonlinear pattern can account for the sometimes conflicting reports of associations between amyloid and fcMRI in individuals with preclinical Alzheimer's disease.