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Building upon our previous work on the Wilson-Cowan equations with distributed delays (Kaslik et al., 2022), we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupling weights and time delay, with the weak Gamma kernel restricting oscillations to a tighter locus of coupling strengths, and to a limited range of time delays. We finally illustrate the general analytical results with simulations for two particular applications: generation of beta-rhythms in the basal ganglia, and alpha oscillations in the prefrontal-limbic system. • We study long-term dynamics in coupled Wilson–Cowan systems with distributed delays. • Our analysis focuses on understanding the system's transitions in and out of stable oscillations. • We study how these transitions change under different connectivity schemes and strengths. • We explore the effects of different delay distributions and average delay values. • The analysis is illustrated with simulations in two different functional brain networks. [ABSTRACT FROM AUTHOR]