[en] Results of a ²⁰⁸ Pb (γ,γ') experiment are presented aiming at an identification of the 2 ⁺ member of the long-sought two-octupole phonon multiplet. Four E2 excitations have been observed below 6.5 MeV excitation energy, two of them for the first time. However, in contrast to new results of calculations within the quasiparticle-phonon nuclear model (QPM), no obvious candidate for the two-octupole phonon vibration could be found in the present study. We discuss the J^π=2⁺ states detected in this as well as previous experiments with respect to their possible two-octupole phonon structure