  The double-electron capture and the electron capture with positron emission
in $^{168}$Yb have been investigated for the first time at the STELLA facility
of the Gran Sasso underground laboratory (Italy) measuring 371 g of highly
purified ytterbium oxide placed on the end-cap of a 465 cm$^3$
ultra-low-background high purity Germanium detector (HPGe). No gamma associated
to double beta processes in $^{168}$Yb have been observed after 2074 h of data
taking. This has allowed setting the half-life limits on the level of $\lim
T_{1/2}\sim$ $10^{14}-10^{18}$ yr at 90\% C.L. Particularly, a lower half-life
limit on a possible resonant neutrinoless double-electron capture in $^{168}$Yb
to the $(2)^-$ 1403.7 keV excited state of $^{168}$Er is set as
$T_{1/2}\geq1.9\times 10^{18}$ yr at 90\% C.L. Half-life limits
$T_{1/2}^{2\nu(0\nu)}\geq 4.5(4.3)\times10^{16}$ yr were set on the
$2\nu(0\nu)2\beta^-$ decay of $^{176}$Yb to the $2^+$ 84.3 keV first excited
level of $^{176}$Hf.
