  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.
