  The first ever search for $2\varepsilon$ and $\varepsilon\beta^+$ decay of
$^{174}$Hf was realized using a high-pure sample of hafnium (with mass 179.8 g)
and the ultra low-background HPGe-detector system located 225 m underground.
After 75 days of data taking no indication of the double beta decay transitions
could be detected but lower limits for the half-lives of the different channels
and modes of the decays were set on the level of $\lim T_{1/2}\sim
10^{16}-10^{18}$ a.
