The first ever search for α 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 α decay to the ground state of 175 Yb was searched for thanks to the β-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 ∼ 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 ≥ 3.3 × 10 15 a.