  High quality electron-doped HTSC single crystals of $\rm
Pr_{2-x}Ce_{x}CuO_{4+\delta}$ and $\rm Nd_{2-x}Ce_{x}CuO_{4+\delta}$ have been
successfully grown by the container-free traveling solvent floating zone
technique. The optimally doped $\rm Pr_{2-x}Ce_{x}CuO_{4+\delta}$ and $\rm
Nd_{2-x}Ce_{x}CuO_{4+\delta}$ crystals have transition temperatures $T_{\rm c}$
of $25$\,K and $23.5$\,K, respectively, with a transition width of less than
$1$\,K. We found a strong dependence of the optimal growth parameters on the Ce
content $x$. We discuss the optimization of the post-growth annealing treatment
of the samples, the doping extension of the superconducting dome for both
compounds as well as the role of excess oxygen. The absolute oxygen content of
the as-grown crystals is determined from thermogravimetric experiments and is
found to be $\ge 4.0$. This oxygen surplus is nearly completely removed by a
post-growth annealing treatment. The reduction process is reversible as
demonstrated by magnetization measurements. In as-grown samples the excess
oxygen resides on the apical site O(3). This apical oxygen has nearly no doping
effect, but rather influences the evolution of superconductivity by inducing
additional disorder in the CuO$_{2}$ layers. The very high crystal quality of
$\rm Nd_{2-x}Ce_{x}CuO_{4+\delta}$ is particularly manifest in magnetic quantum
oscillations observed on several samples at different doping levels. They
provide a unique opportunity of studying the Fermi surface and its dependence
on the carrier concentration in the bulk of the crystals.
