Alzheimer's disease (AD) is characterized by two hallmark molecular pathologies: amyloid aβ1-42, and Tau neurofibrillary tangles. To date, studies of functional connectivity MRI (fcMRI) in preclinical AD have relied on associations with in-vivo measures of amyloid pathology. With the recent advent of in-vivo 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 (DMN), Salience, Dorsal Attention (DAN), and Frontoparietal Control (FPCN)) as a function of global cortical amyloid (PiB-PET) and regional Tau (AV1451-PET) in entorhinal, inferior temporal (IT), and inferior parietal (IP) 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 hyper-connectivity phase followed by a hypo-connectivity phase in the course of preclinical AD.Significance: This paper offers a first look at the relationship between Tau-PET imaging with F(18)-AV1451 and functional connectivity MRI (fcMRI) in the context of amyloid-PET imaging. The results suggest a non-linear 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 hyper- and hypo- connectivity. Furthermore, this nonlinear pattern can account for the sometimes conflicting reports of associations between amyloid and fcMRI in preclinical AD.