We have studied the evolution, with hydrostatic pressure, of the recently discovered superconductivity in the graphite intercalation compounds C$_6$Yb and C$_6$Ca. We present pressure-temperature phase diagrams, for both superconductors, established by electrical transport and magnetization measurements. In the range 0-1.2 GPa the superconducting transition temperature increases linearly with pressure in both materials with $dT_c/dP = +0.39 K/GPa$ and $dT_c/dP = +0.50 K/GPa$ for C$_6$Yb and C$_6$Ca respectively. The transition temperature in C$_6$Yb, which has beenmeasured up to 2.3 GPa, reaches a peak at around 1.8 GPa and then starts to drop. We also discuss how this pressure dependence may be explained within a plasmon pairing mechanism.
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