In the brain, while early sensory areas encode and process external inputs rapidly, higher-association areas are endowed with slow dynamics to benefit information accumulation over time. This property raises the question of why diverse timescales are well localized rather than being mixed up across the cortex, despite high connection density and an abundance of feedback loops that support reliable signal propagation. In this talk, we will address this question by analyzing a large-scale network model of the primate cortex, and we identify a novel dynamical regime termed "interference-free propagation". In this regime, the mean components of the synaptic currents to each downstream area are imbalanced to ensure signals to propagate reliably, while the temporally fluctuating components of the synaptic inputs governed by upstream areas' timescales are largely canceled out, leading to the localization of its own timescale in each downstream area. Our result provides new insights into the operational regime of the cortex, leading to the coexistence of hierarchical timescale localization and reliable signal propagation.