There is an urgent need to understand the relationships between amyloid- (A) and tau in the progression of Alzheimer's disease to identify treatment targets. Here we examine reciprocal predictions of brain A burden quantified by positron emission tomography and CSF concentrations of A42 and phosphorylated tau (p-tau). Each biomarker was examined over 48 months in two separate cross-lagged models; one in asymptomatic healthy elderly people (men and women), and one in patients with Alzheimer's disease (AD) dementia or mild cognitive impairment (MCI). The models examine predictions of each biomarker on the progression of the others, considering each previous and concurrent measure. In healthy elderly, lower CSF A42 predicted A deposition and reciprocally, A burden predicted a decrease in CSF A42. Lower CSF A42 predicted an increase in CSF p-tau, and CSF p-tau predicted A deposition. In AD/MCI, lower CSF A42 predicted A deposition and A burden reciprocally predicted CSF A42 changes; however, in contrast to healthy elderly, CSF p-tau concentrations did not predict A biomarkers, or vice versa. In post hoc models examining cognitive status, CSF A42 predicted Mini Mental State Examination (MMSE) scores in healthy elderly, whereas A burden and CSF p-tau predicted MMSE scores in AD/MCI. The findings describe reciprocal predictions between A and tau biomarkers in healthy elderly and they implicate mechanisms underlying low CSF A42 in Alzheimer's disease pathogenesis and progression. In symptomatic Alzheimer's disease, CSF A42 and A deposition predicted each other; however, A and CSF p-tau progressed independently and they independently predicted cognitive decline.