17Functional neuronal correlations between pairs of neurons are thought to play an important 18 role in neuronal information processing and optimal neuronal computations during attention, 19 perception, decision-making and learning. Here, we report dynamic changes in prefrontal 20 neuronal noise correlations at multiple time-scales, as a function of task contingencies. 21 Specifically, we record neuronal activity from the macaque frontal eye fields, a cortical region 22 at the source of spatial attention top-down control, while the animals are engaged in tasks of 23 varying cognitive demands. We show that the higher the task demand and cognitive 24 engagement the lower noise correlations. We further report that within a given task, noise 25 correlations significantly decrease in epoch of higher response probability. Last we show that 26 the power of the rhythmic modulations of noise correlations in the alpha and beta frequency 27 ranges also decreases in the most demanding tasks. All of these changes in noise correlations 28 are associated with layer specific modulations in spikes-LFP phase coupling, suggesting both 29 a long-range and a local intra-areal origin. Over all, this indicates a highly dynamic 30 adjustment of noise correlations to ongoing task requirements and suggests a strong functional 31 role of noise correlations in cognitive flexibility. 32 33 Significance statement 34 Cortical neurons are densely interconnected. As a result, pairs of neurons share some degree 35 of variability in their neuronal responses. This impacts how much information is present 36 within a neuronal population and is critical to attention, decision-making and learning. Here 37 we show that, in the prefrontal cortex, this shared inter-neuronal variability is highly flexible, 38 decreasing across tasks as cognitive demands increase and within trials in epochs of maximal 39 behavioral demand. It also fluctuates in time at a specific rhythm, the power of which 40 decreases for higher cognitive demand. All of these changes in noise correlations are 41 associated with layer specific modulations in spikes-LFP phase coupling. Over all, this 42 suggests a strong functional role of noise correlations in cognitive flexibility. 43 44 45 46 Optimal behavior is the result of interactions between neurons both within and across 47 brain areas. Identifying how these neuronal interactions flexibly adjust to the ongoing 48 behavioral demand is key to understand the neuronal processes and computations underlying 49 optimal behavior. Several studies have demonstrated that functional neuronal correlations 50 between pairs of neurons, otherwise known as noise correlations, play an important role in 51 perception and decision-making 1-9 . Specifically, several experimental and theoretical studies 52 show that noise correlations have an impact on the amount of information that can be decoded 53 for neuronal populations 4,10-12 as well as on overt behavioral performance 4,10-15 . As a result, 54 understanding how noise correlations dynamica...