We study the nature of the low-lying resonance states in mirror nuclei 9 Be and 9 B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides a convenient description of the three-cluster continuum. The dominant three-cluster configurations α + α + n and α + α + p in 9 Be and 9 B, respectively, are taken into account. Dominant decay channels for all resonance states in 9 Be and 9 B are explored. Much attention is paid to the controversial 1/2 + resonance states in both nuclei. We study effects of the Coulomb interaction on the energy and width of three-cluster resonances in the mirror nuclei 9 Be and 9 B. We also search for the Hoyle-analog state, which is a key step for alternative ways to synthesize 9 Be and 9 B in triple collisions of clusters in a stellar environment.