  The first ever search for $\alpha$ decays to the first excited state in Yb
was performed for six isotopes of hafnium (174, 176, 177, 178, 179, 180) using
a high purity Hf-sample of natural isotopic abundance with a mass of 179.8 g.
For $^{179}$Hf, also $\alpha$ decay to the ground state of $^{175}$Yb was
searched for thanks to the $\beta$-instability of the daughter nuclide
$^{175}$Yb. The measurements were conducted using an ultra low-background
HPGe-detector system located 225 m underground. After 75 d of data taking no
decays were detected but lower bounds for the half-lives of the decays were
derived on the level of $\lim T_{1/2}\sim 10^{15}-10^{18}$~a. The decay with
the shortest half-life based on theoretical calculation is the decay of
$^{174}$Hf to the first $2^+$ 84.3~keV excited level of $^{170}$Yb. The
experimental lower bound was found to be $T_{1/2}\geq 3.3\times 10^{15}$ a.
