The optical coupled resonant system consisting of an integrated resonator with gain and a resonator with loss provides an excellent platform to create exceptional points (EPs) in non-Hermitian systems. Most previous studies have focused on the striking intensity feature of EPs, but its phase response is seldom investigated. In this work, we present a thorough study on the phase response of an EP system. Intriguingly, the phase response exhibits distinct behavior depending on the ordering of the ring resonators: when the input light in a bus waveguide is coupled directly or indirectly to the ring with a gain, the phase response is featured by nonmonotonic transition and 2π monotonic transition, respectively. We also prove that the newly identified phase features are theoretically guaranteed. These phase responses produce unique group delays that have never been found in other coupled resonant systems. The results deepen our understanding on EPs in non-Hermitian systems and are potentially useful for practical applications exploiting phase features.