  A search for alpha and double beta decays of ytterbium isotopes was performed
with an ultra-low background high purity germanium detector at Gran Sasso
Underground Laboratory (Italy). A 194.7 g Yb$_2$(C$_2$O$_4$)$_3$ powder sample
was measured for 11.3~d with a total Yb exposure of 1.25 kg$\times$d. Half-life
limits for $\alpha$-decay modes of $^{168}$Yb, $^{170}$Yb, $^{171}$Yb,
$^{172}$Yb, $^{173}$Yb, $^{174}$Yb and $^{176}$Yb into the first excited states
have been obtained between $6\times10^{14}$ yr and $2\times10^{16}$ yr. These
are the first experimental constraints of these decay modes. Double electron
capture of $^{168}$Yb and double beta decay of $^{176}$Yb into the first
excited 2$^+$ and 0$^+$ states could be excluded with limits between
$1\times10^{14}$ yr to $8\times10^{16}$ yr. This improves the experimental
information on some of the decay modes compared to previous constraints.
