The GRACE mission consists of two identical satellites orbiting the Earth at an altitude of ~500 km. Dual-frequency carrier-phase Global Positioning System (GPS) receivers are flying on both satellites. They are used for precise orbit determination and to time-tag the K-band ranging system used to measure changes in the distances between the two satellites. The satellites are also flying ultra-stable oscillators (USOs) to achieve the mission's need for short-term (<1 s) oscillator stability. Because of the high quality of both the GPS receivers and the oscillators, relativistic effects in the GRACE GPS data can be examined. An expression is developed for relativistic effects that explicitly includes the effects of the Earth's oblateness (J₂). Use of this expression significantly reduces the twice per orbital period energy in the GRACE clock solutions, indicating that the effect of J₂ can be significant and should be modeled for satellite clocks in low Earth orbit. After relativistic effects have been removed, both GRACE USOs show large (2 ns to 3 ns) once per orbital period signatures that correlate with voltage variations on the spacecraft.