  The relaxation of Yb$^{3+}$ in YBa$_{2}$Cu$_{3}$O$_{x}$ ($6<x<7$) was studied
using Electron Paramagnetic Resonance (EPR). It was found that both electronic
and phononic processes contribute to the Yb$^{3+}$ relaxation. The phononic
part of the relaxation has an exponential temperature dependence, which can be
explained by a Raman process via the coupling to high-energy ($\sim$500 K)
optical phonons or an Orbach-like process via the excited vibronic levels of
the Cu$^{2+}$ ions (localized Slonczewski-modes). In a sample with a maximum
oxygen doping $x$=6.98, the electronic part of the relaxation follows a
Korringa law in the normal state and strongly decreases below $T_{c}$.
Comparison of the samples with and without Zn doping proved that the
superconducting gap opening is responsible for the sharp decrease of Yb$^{3+}$
relaxation in YBa$_{2}$Cu$_{3}$O$_{6.98}$. It was shown that the electronic
part of the Yb$^{3+}$ relaxation in the superconducting state follows the same
temperature dependence as $^{63}$Cu and $^{17}$O nuclear relaxations despite
the huge difference between the corresponding electronic and nuclear relaxation
rates.
