This paper investigates the effect gain and phase margins (GPM) on delay-dependent stability analysis of a two-area load frequency control (LFC) system with communication delays. An frequency-domain based exact method that takes into account both gain and phase margins is utilized to determine stability delay margins in terms of system and controller parameters. A gain-phase margin tester (GPMT) is introduced to the LFC system as to take into gain and phase margins in delay margin computation. For a wide range of proportional - integral (PI) controller gains, time delay values at which LFC system is both stable and have desired stability margin measured by gain and phase margins are computed. The time-domain simulation studies indicate that delay margins must be determined considering gain and phase margins to have a better dynamic performance in term of fast damping of oscillations, less overshoot and settling time.